NCERT Solutions for Class 8 Maths Chapter 14 Factorization

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# NCERT Solutions for Class 8 Maths Chapter 14 Factorization

Edited By Ramraj Saini | Updated on Oct 09, 2023 07:16 PM IST

## NCERT Solutions for Class 8 Maths Chapter 14 Factorization

Factorization Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at craeers360 keeping in mind of the latest syllabus and pattern of CBSE 2023-23. In NCERT solutions for Class 8 Maths chapter 14 Factorization, you will be dealing with questions related to algebraic expressions and natural numbers. Important topics like methods of common factors, factorization using identities, factorization by regrouping terms, factors of the form (x + a) ( x + b), and division of algebraic expressions are covered in this chapter.

There are 4 exercises with 34 questions given in the NCERT textbook. All these questions are prepared in the solutions of NCERT for Class 8 Maths chapter 14 Factorization in a step-by-step manner. It will be easy for you to understand the concept. For a better understanding of the concept, there are some practice questions given after every topic. You will find solutions to these practice questions also in NCERT Solutions for Class 8 maths by clicking on the link.

## Factorization Class 8 Solutions - Important Formulae

Factorization: Factorization is the process of expressing an algebraic equation as a product of its components. These components can be numbers, variables, or algebraic expressions.

Irreducible Factor: An irreducible factor is a component that cannot be further factored into a product of factors.

Method to Do Factorization:

The common factor approach involves three steps:

Write each term of the statement as a product of irreducible elements.

Look for and separate the similar components.

Combine the remaining elements in each term using the distributive law.

The regrouping approach involves grouping terms in a way that brings out a common factor across the groups.

Common Factor Identity: Certain factorable expressions take the form of:

• a2 + 2ab + b2 = (a + b)2

• a2 - 2ab + b2 = (a - b)2

• a2 - b2 = (a + b)(a - b)

• x2 + (a + b)x + ab = (x + a)(x + b)

Dividing a Polynomial by a Monomial: When dividing a polynomial by a monomial, you can divide each term of the polynomial by the monomial or use the common factor technique.

Division of Algebraic Expressions: In division of algebraic expressions, you factor both the dividend and the divisor, then cancel common factors.

Division Formula: Dividend = Divisor × Quotient or Dividend = Divisor × Quotient + Remainder.

Free download NCERT Solutions for Class 8 Maths Chapter 14 Factorization for CBSE Exam.

## Factorization Class 8 NCERT Solutions (Intext Questions and Exercise)

NCERT Solutions for Class 8 Maths Chapter 14 Factorization - Topic 14.2.1 Method Of Common Factor

Question:(i) Factorise:

We have
$12x = 2 \times 2 \times 3 \times x$
$36 = 2 \times 2 \times 3 \times 3$

So, we have $2 \times 2 \times 3$ common in both
Therefore,

$12x + 36 =$ $2 \times 2 \times 3 (x + 3)$

$12x + 36 = 12(x + 3)$

Question:(ii) Factorise : 22y-32z

We have,
$22y=$ $2 \times 11 \times y$
$33z =$ $3 \times 11 \times z$
So, we have 11 common in both
Therefore,

$22y - 33z = 11(2y - 3z)$

Question:(iii) Factorise :

We have
$14pq =$ $2 \times 7 \times p \times q$
$35pqr =$ $5 \times 7 \times p \times q \times r$
So, we have

$7 \times p \times q$ common in both
Therefore,

$14pq + 35pqr =7pq (2 + 5r)$

Class 8 maths chapter 14 question answer - Exercise: 14.1

Question:1(i) Find the common factors of the given terms.

We have
$12x ={\color{Red} 2 \times 2 \times 3}\times x$
$36 = {\color{Red} 2 \times 2 \times 3}\times 3$
So, the common factors between the two are

$2\times2\times3=12$

Question:1(ii) Find the common factors of the given terms

We have,
$2y = {\color{Red} 2 \times y}$
$22xy = {\color{Red} 2} \times 11 \times x {\color{Red} \times y}$
Therefore, the common factor between these two is 2y

Question:1(iii) Find the common factors of the given terms

We have,
$14pq = {\color{Red} 2 \times 7 \times p \times q}$
$28p^2q^2 = 2 \times {\color{Red} 2 \times 7 \times p} \times p{\color{Red} \times q} \times q$
Therefore, the common factor is

$2\times7\times p\times q=14pq$

Question:1(iv) Find the common factors of the given terms.

We have,
$2x = 2 \times x$
$3x^2 = 3 \times x \times x$
$4 = 2 \times 2$
Therefore, the common factor between these three is 1

Question:1(v) Find the common factors of the given terms

We have,
$6abc ={\color{Red} 2 \times 3 \times a \times b }\times c$
$24ab^2 = 2 \times 2\times {\color{Red} 2\times 3 \times a \times b} \times b$
$12a^2b = 2 \times {\color{Red} 2\times 3 \times a} \times a{\color{Red} \times b}$
Therefore, the common factors is

$2 \times 3 \times a \times b = 6ab$

Question:1(vi) Find the common factors of the given terms

We have,
$16x^3 = 2 \times 2 \times {\color{Red} 2 \times 2 \times x} \times x \times x$
$4x^2 = {\color{Red} 2 \times 2 \times x} \times x$
$32x = 2 \times 2 \times 2 \times{\color{Red} 2 \times 2 \times x}$
Therefore, the common factors is

$2 \times 2 \times x = 4x$

Question:1(vii) Find the common factors of the given terms

We have,
$10pq ={\color{DarkRed} 2 \times 5} \times p \times q$
$20qr = 2\times{\color{DarkRed} 2 \times 5 }\times q \times r$
$30rp ={\color{DarkRed} 2}\times 3{\color{DarkRed} \times 5} \times r \times p$
Therefore, the common factors between these three is

$2 \times 5 =10$

Question:1(viii) Find the common factors of the given terms

$(viii)3 x ^2 y^3 , 10 x ^3 y ^ 2 , 6 x^ 2 y^2 z$

We have,
$3x^{2}y^{2}$ $= 3 \times {\color{Red} x \times x \times y \times y}$
$10x^{3}y^{2}$ $=2 \times 5 \times x \times {\color{Red} x\times x \times y \times y}$
$6x^{2}y^{2}z$ $=2 \times 3 \times{\color{Red} x \times x \times y \times y} \times z$
Therefore, the common factors between these three are $x\times x\times y \times y =$ $x^{2}y^{2}$

Question:2(i) Factorise the following expressions

We have,
$7x = 7 \times x \\ 42=7\times 2 \times 3=7\times 6\\ 7x-42=7x-7\times 6=7(x-6)$

Therefore, 7 is a common factor

Question:2(ii) Factorise the following expressions

We have,
$6p = 2 \times 3 \times p$
$12q = 2 \times 2 \times 3 \times q$
$\therefore$ on factorization

$6p -12q = (2\times 3 \times p) - (2\times 2 \times 3 \times q) = (2\times 3)(p-2q) = 6(p-2q)$

Question:2(iii) Factorise the following expressions

We have,
$7a^2 = 7 \times a \times a$
$14a = 2 \times 7 \times a$
$\therefore$ $7a^2+14a = (7\times a \times a)+(2 \times 7 \times a) = (7 \times a)(a+2)$
$= 7a(a+2)$

Question:2(iv) Factorise the following expressions

We have,
$-16z = -1 \times 2 \times 2 \times 2 \times 2 \times z$
$20z^3 = 2 \times 2 \times 5 \times z \times z \times z$
$\therefore$ on factorization we get,
$-16z+20z^3 = (-1 \times 2 \times 2 \times 2 \times 2 \times z)+(2 \times 2 \times 5 \times z \times z \times z )$
$= (2\times 2 \times z)(-1 \times 2 \times 2+ 5 \times z \times z )$
$= 4z(-4+5z^2 )$

Question:2(v) Factorise the following expressions

We have,
$20l^2m = 2 \times 2 \times 5 \times l \times l \times m$
$30alm = 2 \times 3 \times 5 \times a \times l \times m$
$\therefore$ on factorization we get,
$20l^2m+30alm =(2\times 2 \times 5 \times l \times l \times m) + (2 \times 3 \times 5 \times a \times l \times m)$
$=(2\times 5 \times l \times m)(2\times l + 3 \times a )$
$=10lm(2l+3a)$

Question:2(vi) Factorise the following expressions

We have,
$5x^2y = 5 \times x\times x \times y$
$15xy^2 =3\times 5 \times x\times y \times y$
$\therefore$ on factorization we get,
$5x^2y - 15xy^2 = (5 \times x \times x \times y ) - (3\times 5 \times x \times y \times y )$
$=(5\times x \times y) ( x - 3\times y )$
$=5xy (x-3y)$

Question:2(vii) Factorise the following expressions

We have,
$10a^2 = 2 \times 5 \times a \times a$
$15b^2 = 3 \times 5 \times b \times b$
$20c^2 = 2\times 2 \times 5 \times c \times c$
$\therefore$ on factorization we get,
$10a^2-15b^2+20c^2 = (2\times 5 \times a \times a)-(3\times 5 \times b \times b)+(2\times 2 \times 5 \times c \times c)$ $=5 (2 \times a \times a-3 \times b \times b+2\times 2 \times c \times c)$
$=5(2a^2-3b^2+4c^2)$

Question:2(viii) Factorise the following expressions

We have,
$-4a^2 = -1\times 2 \times 2 \times a\times a$
$4ab = 2 \times 2 \times a\times b$
$4ca = 2 \times 2 \times c\times a$
$\therefore$ on factorization we get,
$-4a^2+4ab-4ca = (-1 \times 2 \times 2 \times a\times a )+( 2 \times 2 \times a\times b )- (2 \times 2 \times c\times a)$

$=(2 \times 2 \times a) (-1 \times a + b - c)$
$= 4a(-a+b-c)$

Question:2(ix) Factorise the following expressions

We have,
$x^2yz =x \times x \times y \times z$
$xy^2z =x \times y \times y \times z$
$xyz^2 =x \times y \times z \times z$
Therefore, on factorization we get,
$x^2yz+xy^2z+xyz^2 =(x \times x \times y \times z)+(x \times y \times y \times z)+(x \times y \times z \times z)$

$=( x \times y \times z)(x + y + z)$
$=xyz(x+y+z)$

Question:2(x) Factorise the following expressions

We have,
$ax^2y = a \times x \times x \times y$
$bxy^2 = b \times x \times y \times y$
$cxyz = c \times x \times y \times z$
Therefore, on factorization we get,
$ax^2y+bxy^2+cxyz = ( a \times x \times x \times y)+( b \times x \times y \times y)+(c \times x \times y \times z)$ $= (x\times y)( a \times x+ b \times y+c \times z)$

$= xy(ax+by+cz)$

We have,
$x^2 = x \times x$
$xy = x \times y$
$8x = 8 \times x$
$8y = 8 \times y$
Therefore, on factorization we get,
$x^2+xy+8x+8y = (x \times x)+(x\times y )+(8 \times x)+(8 \times y)$
$= x(x +y )+8(x+ y)$
$= (x+8)(x+y)$

Question:3(ii) Factorise

We have,
$15xy = 3 \times 5 \times x \times y$
$6x = 2 \times 3 \times x$
$5y = 5 \times y$
$2 = 2$
Therefore, on factorization we get,
$15xy - 6x +5y-2 = (3\times 5 \times x \times y)-(2 \times 3 \times x)+(5\times y)-2$
$=(5 \times y)(3\times x + 1)-2(3\times x + 1)$
$=(5y-2)(3x+1)$

Question:3(iii) Factorise

We have,
$ax+bx-ay-by = a(x-y)-b(x-y)$
$=(a-b)(x-y)$
Therefore, on factorization we get,
$(a-b)(x-y)$

Question:3(iv) Factorise

We have,
$15pq + 15 + 9q + 25p = 5 p(3q + 5) + 3 (3q + 5)$
$= (3q + 5)(5p + 3)$
Therefore, on factorization we get,
$(3q + 5)(5p + 3)$

Question:3(v) Factorise

We have,
$z - 7 + 7xy - xyz = z(1 - xy) -7(1 - xy)$
$= (1 - xy)(z - 7)$
Therefore, on factorization we get,
$(1 - xy)(z - 7)$

Class 8 maths chapter 14 NCERT solutions - Exercise: 14.2

Question:1(i) Factorise the following expressions

We have,
$a^2 + 8a + 16 = a^2+ 4a + 4a + 16$
$= a(a + 4) + 4 (a+4)$
$= (a+4)(a+4) =$ $(a+4)^{2}$
Therefore,
$a^2+8a+16 = (a+4)^2$

Question:1(ii) Factorise the following expressions

We have,
$p^2 - 10p + 25 = p^2 - 5p - 5p + 25$
$= p(p - 5) -5 (p -5)$
$= (p - 5)(p - 5) =$ $(p-5)^{2}$
Therefore,
$p^2-10p+25 =(p-5)^2$

Question:1(iii) Factorise the following expressions

We have,
$25m^2 + 30m + 9 = 25m^2 + 15m + 15m + 9$
$= 5m (5m + 3) +3(5m + 3)$
$= (5m + 3) (5m + 3) =$ $(5m+3)^{2}$
Therefore,
$25m^2+30m+9 = (5m+3)^2$

Question:1(iv) Factorise the following expressions

We have,
$49 y^2 + 84 yz + 36 z^2$ $= 49y^2 + 42yz + 42yz + 36z^2$
$= 7y(7y + 6z) + 6z(7y + 6z)$
$= (7y + 6z)(7y + 6z) =$ $(7y+ 6z)^{2}$
Therefore,
$49y^2+84yz+36z^2=(7y+6z)^2$

Question:1(v) Factorise the following expressions

We have,
$4 x^2 - 8x + 4$ $= 4x^2 - 4x - 4x + 4$
$= 4x(x - 1) -4(x - 1)$
$= 4(x-1)(x-1) \\\ \ \ = 4(x-1)^{2}$

Question:1(vi) Factorise the following expressions

We have,
$121 b^2 - 88 bc + 16 c^2$ $= 121b^2 - 44bc - 44bc + 16c^2$
$= 11b(11b - 4c) - 4c(11b - 4c)$
$= (11b-4c)(11b-4c) =$ $(11b -4c)^{2}$
Therefore,
$121 b^2 - 88 bc + 16 c^2$ $=$ $(11b -4c)^{2}$

Question:1(vii) Factorise the following expressions

We have,
$( l+m ) ^2 - 4lm$ = $l^{2} + 2ml + m^{2} - 4lm$ $(using \ (a+b)^{2} = a^{2} + 2ab + b^{2})$
= $l^{2} - 2lm + m^{2}$
= $(l-m)^{2}$ $(using \ (a-b)^{2} = a^{_2} -2ab + b^{2})$

Question:1(viii) Factorise the following expressions

We have,
$a ^4 +2 a ^2 b ^ 2 + b ^ 4$ = $a^{4}$ + $a^{2}b^{2}$ + $a^{2}b^{2}$ + $b^{4}$
= $a^{2}(a^{2 }+ b^{2}) + b^{2}(a^{2}+b^{2})$ = $(a^{2}+b^{2})(a^{2}+b^{2})$ = $(a^{2}+b^{2})^{2}$

Question:2(i) Factorise :

This can be factorized as follows
$4 p^2 - 9 q ^2$ = $(2p)^{2} - (3q)^{2}$ $= (2p - 3q)(2p + 3q)$ $(using \ (a)^{2} - (b)^{2} = (a-b)(a+b))$

Question:2(ii) Factorise the following expressions

We have,
$63 a ^2 - 112 b ^ 2$ $= 7$ $(9a^{2} - 16b^{2})$ $= 7$ $((3a)^{2} - (4b)^{2})$ $=7 (3a - 4b)(3a + 4b)$
$(using \ (a)^{2} - (b)^{2} = (a-b)(a+b))$

Question:2(iii) Factorise

This can be factorised as follows
$49 x^2 - 36$ = $(7x)^{2} - (6)^{2}$ $= (7x - 6)(7x + 6)$ $(using \ (a)^{2} - (b)^{2} = (a-b)(a+b) )$

Question:2(iv) Factorise

The given question can be factorised as follows
$16 x^5 - 144 x ^ 3$ $= 16x^3(x^{2}- 9)$
$= 16x^3((x)^{2}- (3)^{2})$ $= 16x^3(x-3)(x+3)$ $(using \ (a)^{2}- (b)^{2} = (a-b)(a+b))$

Question:2(v) Factorise

We have,
$(l+m) ^ 2 - ( l- m ) ^2$ $= [(l + m) - (l - m)][(l + m) + (l - m)]$ (using $a^{2} - b^{2} = (a-b)(a+b)$ )
$= (l + m - l + m)(l + m + l - m)$
$= (2m)(2l) = 4ml$

Question:2(vi) Factorise

We have,
$9 x ^2 y^2 - 16$ = $(3xy)^{2} -(4)^{2}$ (using $(a)^{2} -(b)^{2} = (a-b) (a+b)$ )
$= (3xy - 4 )(3xy + 4)$

Question:2(vii) Factorise

We have,
$( x ^2 -2xy + y^2 ) - z ^2$ = $(x-y)^{2} - z^{2}$ $(using \ (a-b)^{2} = a^{2} -2ab + b^{2})$
$= (x - y - z)(x - y + z)$ $(using \ (a)^{2} - (b)^{2} = (a -b ) (a+b))$

Question:2(viii) Factorise

We have,
$25 a ^2 -4 b ^2 + 28 bc - 49 c ^2$ = $25a^{2} - (2b-7c)^{2}$ $(using \ (a-b)^{2} = a^{2} -2ab + b^{2})$
= $(5a)^{2} - (2b-7c)^{2}$ $(using \ (a)^{2} - (b)^{2} = (a -b ) (a+b))$
$=(5a - (2b - 7c))(5a + (2b - 7c)$ )
$= (5a - 2b + 7c)(5a + 2b - 7c )$

Question:3(i) Factorise the following expressions

We have,
$ax^2 = a \times x \times x$
$bx = b \times x$
Therefore,
$ax ^2 + bx$ $= (a \times x \times x) + (b \times x)$
$= x(a \times x + b)$
$= x(ax + b)$

Question:3(ii) Factorise the following expressions

We have,
$7p^2 = 7 \times p \times p$
$21q^3 = 3 \times 7 \times q \times q$
Therefore,
$7p^2 + 21 q ^2$ $= (7 \times p \times p) + (3 \times 7 \times q \times q)$
$=7$ $(p^{2}+ 3q^{2})$

Question:3(iii) Factorise the following expressions

We have,
$2x^3 = 2 \times x \times x \times x$
$2xy^2 = 2 \times x \times y \times y$
$2xz^2 = 2 \times x \times z \times z$
Therefore,
$2 x^3 + 2xy^2 + 2 xz ^2$ $= (2 \times x \times x \times x) + ( 2 \times x \times y \times y) + ( 2 \times x \times z \times z)$
$= (2 \times x) [(x \times x) + (y \times y ) + (z \times z)]$
$= 2x(x^2+y^2+z^2)$

Question:3(iv) Factorise the following expressions

$am^2 + bm ^2 + bn ^2 + an^2$

We have,
$am^2 + bm ^2 + bn ^2 + an^2$ $= m^2(a + b) + n^2(a + b)$
$= (a + b)$ $(m^{2 }+n^{2})$

Question:3(v) Factorise the following expressions

We have,
$( lm + l ) + m + 1$ $= lm + l + m + 1$
$= l(m + 1) +1(m + 1)$
$= (m + 1)(l + 1)$

Question:3(vi) Factorise the following expressions

We have,
$y ( y + z ) + 9 ( y + z )$
Take ( y+z) common from this
Therefore,
$y ( y + z ) + 9 ( y + z )$ $= (y + z)(y + 9)$

Question:3(vii) Factorise the following expressions

We have,
$5 y ^ 2 - 20 y - 8z + 2yz$ $= 5y(y - 4) + 2z(y - 4)$
$= (y - 4)(5y + 2z)$
Therefore,
$5 y ^ 2 - 20 y - 8z + 2yz$ $= (y - 4)(5y + 2z)$

Question:3(viii) Factorise

We have,
$10 ab + 4a + 5b + 2$ $= 2a(5b + 2) + 1(5b + 2)$
$= (5b + 2)(2a + 1)$
Therefore,
$10 ab + 4a + 5b + 2$ $= (5b + 2)(2a + 1)$

Question:3(ix) Factorise the following expressions

We have,
$6 xy - 4 y + 6 - 9 x$ $= 2y(3x - 2) - 3 (3x - 2)$
$= (3x - 2)(2y - 3)$
Therefore,
$6 xy - 4 y + 6 - 9 x$ $= (3x - 2)(2y - 3)$

We have,
$a ^ 4 - b ^ 4$ = $(a^{2})^{2} - (b^{2})^{2} = (a^{2} - b^{2})(a^{2} + b^{2}) = (a-b)(a+b)(a^{2} + b^{2})$
$using \ (x^{2} - y^{2}) = (x-y)(x+y)$

We have,
$p ^ 4 - 81$ =
$(p^{2})^{2} - (9)^{2} = (p^{2} - 9)(p^{2}+9) \\ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (p^{2}-(3)^{2})(p^{2}+9)\\ .\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (p-3)(p+3)(p^{2}+9)$ $using \ a^{2} - b^{2} = (a-b)(a+b)$

We have,
$x ^4 - ( y + z )^4$ =
$(x^{2})^{2} -((y+z)^{2})^{2} = (x^{2} - (y+z)^{2})(x^{2} +(y+z)^{2})\\ \Rightarrow (x-(y+z))(x+(y+z))(x^{2} +(y+z)^{2})$
$(using \ a^{2} -b^{2} = (a-b)(a+b))$

We have,
$x ^ 4 - ( x-z ) ^ 4$ = $(x^{2})^{2} - ((x-z)^{2})^{2}$ $using \ a^{2}-b^{2} = (a-b)(a+b)$
= $(x^{2} - (x-z)^{2})(x^{2}+(x-z)^{2})$
= $(x+(x-z))(x - (x-z))(x^{2}+(x-z)^{2})$
= $(2x - z)(z)$ $($ $x^{2}+(x-z)^{2}$ $)$

We have,
$a ^ 4 - 2 a^2 b^2 + b ^ 4$ = $a^{4} - a^{2}b^{2} - a^{2}b^{2} + b^{4}$
= $a^{2}(a^{2} - b^{2}) - b^{2}(a^{2} - b^{2})$
= $(a^{2} - b^{2}) (a^{2}-b^{2})$ $using \ a^{2}-b^{2} = (a-b)(a+b)$
= $(a^{2} - b^{2})^{2}$
= $((a - b)(a+b))^{2}$
= $(a - b)^{2}(a+b)^{2}$

Question:5(i) Factorise the following expression

We have,
$p^ 2 + 6 p + 8$ = $p^{2} + 2p + 4p + 8$
$= p(p + 2) + 4(p + 2)$
$=(p + 2)(p + 4)$
Therefore,
$p^ 2 + 6 p + 8$ $=(p + 2)(p + 4)$

Question:5(ii) Factorise the following expression

We have,
$q ^ 2 - 10 q + 21$ = $q^{2} - 7q -3q + 21$
$= q(q - 7) -3(q - 7)$
$=(q - 7)(q - 3)$
Therefore,
$q ^ 2 - 10 q + 21$ $=(q - 7)(q - 3)$

Question:5(iii) Factorise the following expression

We have,
$p^2 + 6 p - 16$ = $p^{2} + 8p - 2p - 16$
$= p(p + 8) -2(p + 8)$
$=(p - 2)(p + 8)$
Therefore,
$p^2 + 6 p - 16$ $=(p - 2)(p + 8)$

Class 8 factorization NCERT solutions - Topic 14.3.1 Division Of A Monomial By Another Monomial

We have,
$\frac{24xy^{2}z^{3}}{6yz^{2}} =\frac{2\times 2\times 2\times3\times y \times y \times z\times z\times z}{2\times 3 \times y \times z \times z}= 4xyz$

We have,
$\frac{63a^{2}b^{4}c^{6}}{7a^{2}b^{2}c^{3}}=\frac{3\times 3 \times 7 \times a \times a \times b \times b\times b^2 \times c \times c \times c \times c^3}{7a^{2}b^{2}c^{3}} = 9b^{2}c^{3}$

NCERT Solutions for Class 8 Maths Chapter 14 Factorization-Exercise: 14.3

Question:1(i) Carry out the following divisions

, $\frac{28x^{4}}{56x} = \frac{2 \times 2 \times 7 \times x \times x \times x \times x}{2 \times 2 \times 2 \times 7 \times x} = \frac{x^{3}}{2}$

This is done using factorization.

Question:1(ii) Carry out the following divisions

We have,
$-36$ $y^{3}$ $= -1 \times 2 \times 2 \times 3 \times 3 \times y \times y \times y$
$9$ $y^{2 }$ $= 3 \times 3 \times y \times y$
Therefore,

$\frac{-36y^{3}}{9y^{2}} = \frac {-1 \times 2 \times 2 \times 3 \times 3 \times y \times y \times y}{3 \times 3 \times y \times y} = -4y$

Question:1(iii) Carry out the following divisions

We have,
$66pq^2r^3 = 2 \times 3 \times 11 \times p \times q \times q \times r \times r \times r$
$11qr^2 = 11 \times q \times r \times r$
Therefore,
$\frac{66pq^{2}r^{3}}{11qr^{2}} = \frac{2 \times 3 \times 11 \times p \times q \times q \times r \times r \times r}{11 \times q \times r \times r} = 6pqr$

Question:1(iv) Carry out the following divisions

We have,

$\therefore \frac{34x^{3}y^{3}z^{3}}{51xy^{2}z^{3}} = \frac{2 \times 17\times \ x \times x \times x \times y \times y \times y \times z\times z \times z}{3 \times 17 \times x \times y \times y \times z \times z\times z} = \frac{2x^{2}y}{3}$

Question:1(v) Carry out the following divisions

We have,

$\frac{12a^8b^8}{-6a^4b^4}= \frac{2 \times 2 \times 3 \times a \times a \times a^{6} \times b \times b \times b \times b \times b^{4}}{-1 \times 2 \times 3 \times a^{6} \times b^{4}} = -2a^{2}b^{4}$

Question:2(i) Divide the given polynomial by the given monomial

We have,
$5x^2 - 6x = x(5x - 6)$

$\therefore \frac{5x^{2}-6}{3x} = \frac{x(5x-6)}{3x} = \frac{5x-6}{3}$

Question:2(ii) Divide the given polynomial by the given monomial

We have,
$3y^{8} - 4y^{6} + 5y^{4} = y^{4}(3y^{4}-4y^{2} + 5)$
$\therefore \frac{y^{4}(3y^{4}-4y^{2}+5)}{y^{4}} = (3y^{4}-4y^{2}+5)$

Question:2(iii) Divide the given polynomial by the given monomial

We have,
$8(x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2} y^{2}z^{3}) = 8x^{2}y^{2}z^{2}(x+y+z)$
$\therefore \frac{8(x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2} y^{2}z^{3})}{4x^{2}y^{2}z^{2}} =\frac{ 8x^{2}y^{2}z^{2}(x+y+z)}{4x^{2}y^{2}z^{2}} =2(x+y+z)$

Question:2(iv) Divide the given polynomial by the given monomial

We have,
$x^{3} + 2x^{2} + 3x = x(x^{2} + 2x + 3)$

$\therefore \frac{x^{3} + 2x^{2} + 3x}{2x} = \frac{x(x^{2} + 2x + 3)}{2x} = \frac{x^{2} + 2x + 3}{2}$

Question:2(v) Divide the given polynomial by the given monomial

We have,
$(p^{3}q^{6} - p^{6}q^{3}) = p^{3}q^{3}(q^{3} - p^{3})$
$\therefore \frac{(p^{3}q^{6} - p^{6}q^{3})}{p^{3}q^{3}} = \frac{p^{3}q^{3}(q^{3} - p^{3})}{p^{3}q^{3}} = (q^{3} - p^{3})$

Question:3(i) workout the following divisions

We have,
$10x -25 = 5(2x - 5)$
Therefore,
$\frac{10x-25}{5}= \frac{5(2x-5)}{5} = 2x - 5$

Question:3(ii) workout the following divisions

We have,
$10x-25 = 5(2x - 5 )$
Therefore,
$\frac{10x-25}{2x-5} = \frac{5(2x-5)}{2x-5} = 5$

Question:3(iii) workout the following divisions

We have,
$10y(6y + 21) = 2 \times y \times 5 \times 3(2y + 7)$
Therefore,
$\frac{10y(6y+21)}{5(2y+7)} = \frac{2 \times 5 \times y \times 3(2y+7)}{5(2y+7)} = 6y$

Question:3(iv) workout the following divisions

We have,
$9x^{2}y^{2}(3z-24) = 9x^{2}y^{2} \times 3(z-8) = 27x^{2}y^{2}(z-8)$

$\therefore \frac{9x^{2}y^{2}(3z-24)}{27xy(z-8)} = \frac{27x^{2}y^{2}(z-8)}{27xy(z-8)} = xy$

Question:3(v) workout the following divisions

We have,
$96abc(3a - 12)(5b - 30) = 2 \times 48abc \times 3(a - 4) \times 5(b - 6)$
$= 2 \times144abc (a - 4) \times 5(b - 6)$
Therefore,
$\frac{96abc(3a-12)(5b-30)}{144(a-4)(b-6)} = \frac{2 \times 144abc (a-4) \times 5 (b - 6)}{144(a-4)(b-6)} = 10abc$

Question:4(i) Divide as directed

We have,
$\frac{5(2x+1)(3x+5)}{2x+1} = 5(3x+5)$

Question:4(ii) Divide as directed

We have,
$\frac{26xy(x+5)(y-4)}{13x(y-4)} = \frac{2 \times 13xy(x+5)(y-4)}{13x(y-4)} =2y(x+5)$

Question:4(iii) Divide as directed

We have,
$\frac{52pqr(p+q)(q+r)(r+p)}{104pq(q+r)(r+p)} = \frac{r(p+q)}{2}$

Question:4(iv) Divide as directed

We have,
$\frac{20(y+4)(y^{2}+5y+3)}{5(y+4)} =\frac{4 \times 5(y+4)(y^{2}+5y+3)}{5(y+4)} = 4(y^{2}+5y+3)$

Question:4(v) Divide as directed

We have,
$\frac{x(x+1)(x+2)(x+3)}{x(x+1)} = (x+2)(x+3)$

Question:5(i) Factorise the expression and divide then as directed

We have,
$\frac{y^{2}+7y+10}{y+5} = \frac{y^{2}+2y +5y +10}{y+5} =\frac{y(y+2)+5(y+2)}{y+5}\\ \\ \Rightarrow \frac{(y+5)(y+2)}{(y+5)} = (y+2)$

Question:5(ii) Factorise the expression and divide then as directed

We have,
$\frac{m^{2}-14m-32}{m+2} = \frac{m^{2}+2m-16m-32}{m+2} = \frac{m(m+2)-16(m+2)}{m+2}\\ \\\Rightarrow \frac{(m-16)(m+2)}{m+2} = m-16$

Question:5(iii) Factorise the expression and divide then as directed

We have,
$\frac{5p^{2}-25p+20}{p-1} = \frac{5p^{2} -5p -20p +20}{p-1} = \frac{5p(p-1)-20(p-1)}{p-1}\\ \\ \frac{(5p-20)(p-1)}{p-1} = 5p-20$

Question:5(iv) Factorise the expression and divide then as directed

We first simplify our numerator
So,
$4yz( z^2+ 6z - 16)$
Add and subtract 64 $\Rightarrow$ $4yz( z^2- 64 + 6z - 16 + 64)$
$= 4yz(z^2-8^2 + 6z + 48)$
$= 4yz((z + 8)(z - 8) + 6(z + 8))$ $using \ a^{2} -b^{2} = (a - b)(a + b)$
$= 4yz (z + 8)(z - 8 + 6)$
$= 4yz(z + 8)(z - 2)$
Now,
$\frac{4yz(z^{2}+6z-16)}{2y(z+8)} = \frac{4yz(z+8)(z-2)}{2y(z+8)}= 2z(z-2)$

Question:5(v) Factorise the expression and divide then as directed

We have,
$\frac{5pq(p^{2} - q^{2})}{2p(p+q)} = \frac{5pq(p-q)(p+q)}{2p(p+q)} \ \ \ \ \ \ \ \ \ \ \ \ \ using \ a^{2}-b^{2} = (a-b)(a+b) \ \ \\. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{5q(p-q)}{2}$

Question:5(vi) Factorise the expression and divide then as directed

We first simplify our numerator,
$12xy$ ( $9x^{2} -16y^{2}$ ) = $12xy$ $(3x)^{2} -(4y)^{2}$

using $(a)^{2} -(b)^{2} = (a-b)(a+b)$
$= 12xy((3x - 4y)(3x + 4y))$
Now,
$\frac{12xy(9x^{2} - 16y^{2})}{4xy(3x + 4y)} = \frac{12xy(3x+4y)(3x-4y)}{4xy(3x+4y)} = 3(3x-4y)$

Question:5(vii) Factorise the expression and divide then as directed

We first simplify our numerator,
$39y^{2}(50y^{2} -98) = 39y^{2} \times 2(25y^{2} - 49)$ using $(a)^{2} -(b)^{2} = (a-b)(a+b)$
= $78y^{2} ((5y)^{2} - (7)^{2})$
= $78y^{2} (5y - 7)(5y+7)$
Now,
$\frac{39y^{2}(50y^{2}-98)}{26y^{2}(5y +7)} = \frac{78y^{2}(5y-7)(5y+7)}{26y^{2}(5y+7)} = 3(5y-7)$

NCERT Solutions for Class 8 Maths Chapter 14 Factorization-Exercise: 14.4

Our L.H.S.
$= 4(x - 5) = 4x - 20$
R.H.S. $= 4x -5$
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is
$4(x - 5) = 4x - 20$

Our L.H.S.
$= x(3x + 2) = 3x^2 + 2x$
R.H.S.= $3x^2 + 2$
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is
$= x(3x + 2) = 3x^2 + 2x$

Our L.H.S. $= 2x + 3y$
R.H.S. = $5xy$
It is clear from the above that L.H.S. is not equal to R.H.S.
SO, correct statement is
$2x + 3y = 2x + 3y$

Our L.H.S. $= x + 2x + 3x = 6x$
R.H.S. $= 5x$
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is
$x + 2x + 3x = 6x$

Our L.H.S. is
$5y + 2y + y - 7y = y$
R.H.S. = 0
IT is clear from the above that L.H.S. is not equal to R.H.S.
So, Correct statement is
$5y + 2y + y - 7y = y$

Our L.H.S. is
$3x + 2x = 5x$
R.H.S. = $5x^2$
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is
$3x + 2x = 5x$

Our L.H.S. is
$(2x)^2 + 4(2x) + 7 = 4x^2 + 8x + 7$
R.H.S. $= 2x^2+8x+7$
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is
$(2x)^2 + 4(2x) + 7 = 4x^2 + 8x + 7$

Our L.H.S. is
$\Rightarrow (2x)^{2}+5x = 4x^2+5x$
R.H.S. = 9x
It is clear from the above that L.H.S. is not equal to R.H.S.
So, the correct statement is
$(2x)^{2}+5x = 4x^2+5x$

LHS IS

$(3x + 2)^{2 } = (3x)^{2} + 2(3x)(2) +(2)^{2}$ using $(a + b)^{2 } = (a)^{2} + 2(a)(b) +(b)^{2}$
$= 9x^2 + 12x + 4$

RHS IS

$3 x ^2 + 6x + 4$

$\boldsymbol{LHS} \neq \boldsymbol{RHS}$

Correct statement is

$(3x + 2)^{2 } = (3x)^{2} + 2(3x)(2) +(2)^{2}$ $= 9x^2 + 12x + 4$

Substituting $x = -3$ in $x ^ 2 + 5 x + 4 \: \: gives \: \: ( -3 ) ^ 2 + 5 ( -3 ) + 4 = 9 + 2 + 4 = 15$

We need to substitute x = -3 in

$x^{2}+5x+4$
$=(-3)^{2}+5(-3)+4$
$= 9 - 15 + 4$
$= -2 \neq 15$

so the given statement is wrong
Correct statement is $(-3)^{2}+5(-3)+4= -2$

We need to substitute x = -3 in $x^2 - 5x + 4$
$= (-3)^2-5(-3) + 4$
$= 9 + 15 + 4=28$
so the given statement is wrong
Correct statement is

$x^2 - 5x + 4=28$

We need to Substitute x = - 3 in $x^{2} + 5x$
= $(-3)^{2} + 5(-3)$
= 9 - 15
= - 6 $\neq$ R.H.S
Correct statement is Substitute x = - 3 in $x^{2} + 5x$ gives -6

Our L.H.S. is $(y - 3 )^{2}$
= $(y )^{2} + 2(y)(-3) + (-3)^{2}$ using $(a-b)^{2} = (a )^{2} + 2(a)(-b) + (-b)^{2}$
= $y^{2}$ $- 6x + 9$ $\neq$ R.H.S.

Correct statement is

$(y - 3 )^{2}$ = $y^{2}$ $- 6x + 9$

Our L.H.S. is $(z+5)^{2}$
= $(z)^{2} + 2(z)(5) + (5)^{2}$ using $(a+b)^{2} = (a)^{2} + 2(a)(b) + (b)^{2}$
= $(z)^{2}$ $+ 10z + 25$ $\neq$ R.H.S.
Correct statement is

$(z+5)^{2}$ = $(z)^{2}$ $+ 10z + 25$

Our L.H.S. is (2a + 3b)(a -b)
= $2a^{2} -2ab + 3ab - 3b^{2}$
= $2a^{2} +ab - 3b^{2}$ $\neq$ R.H.S.
Correct statement is (2a + 3b)(a -b) = $2a^{2} +ab - 3b^{2}$

Oue L.H.S. is (a + 4)(a + 2)
= $a^{2} + 2a + 4a + 8$
= $a^{2} + 6a + 8$ $\neq$ R.H.S.
Correct statement is (a + 4)(a + 2) = $a^{2} + 6a + 8$

Our L.H.S. is (a - 2) (a - 4)
= $a^{2} - 4a - 2a + 8$
= $a^{2} - 6a+ 8$ $\neq$ R.H.S.
Correct statement is (a - 2) (a - 4) = $a^{2} - 6a+ 8$

Our L.H.S. is
$\Rightarrow \frac{3x^{2}}{3x^{2}}$
R.H.S. = 0
It is clear from the above that L.H.S. is not equal to R.H.S.
So, correct statement is
$\frac{3x^{2}}{3x^{2}} = 1$

Our L.H.S. is
$\Rightarrow \frac{3x^2+1}{3x^2}$
R.H.S. = 2
It is clear from the above stattement that L.H.S. is not equal to R.H.S.
So, correct statement is
$\frac{3x^{2}+1}{3x^{2}} = 1 + \frac{1}{3x^{2}} = \frac{3x^{2}+1}{3x^{2}}$

Our L.H.S.

$\Rightarrow \frac{3x}{3x+2}$

R.H.S. = 1/2

It can be clearly observed that L.H.S is not equal to R.H.S

So, the correct statement is,

$\frac{3x}{3x+2} = \frac{3x}{3x+2}$

Our L.H.S. is $\Rightarrow \frac{3}{4x+3} = \frac{3}{4x+3} \neq$ R.H.S.

Correct statement is $\frac{3}{4x+3} = \frac{3}{4x+3}$

Our L.H.S. is $\Rightarrow \frac{4x+5}{4x} = \frac{4x}{4x} + \frac{5}{4x} = 1 + \frac{5}{4x} \neq$ R.H.S.

Correct statement is $\frac{4x+5}{4x} = 1 + \frac{5}{4x} = \frac{4x+5}{4x}$

Our L.H.S. is $\Rightarrow \frac{7x+5}{5} = \frac{7x}{5} + \frac{5}{5} = \frac{7x}{5} + 1 \neq$ R.H.S.

Correct statement is $\frac{7x+5}{5} = \frac{7x}{5} + 1 = \frac{7x+5}{5}$

## Factorization class 8 NCERT solutions - Topics

• What is Factorization?
• Division of Algebraic Expressions
• Division of Algebraic Expressions Continued(Polynomial divide; Polynomial)
• Can you Find the Error?

## NCERT Solutions for Class 8 Maths - Chapter Wise

 Chapter -1 Rational Numbers Chapter -2 Linear Equations in One Variable Chapter-3 Understanding Quadrilaterals Chapter-4 Practical Geometry Chapter-5 Data Handling Chapter-6 Squares and Square Roots Chapter-7 Cubes and Cube Roots Chapter-8 Comparing Quantities Chapter-9 Algebraic Expressions and Identities Chapter-10 Visualizing Solid Shapes Chapter-11 Mensuration Chapter-12 Exponents and Powers Chapter-13 Direct and Inverse Proportions Chapter-14 Factorization Chapter-15 Introduction to Graphs Chapter-16 Playing with Numbers

## Key Features of Factorization Class 8 Solutions

Comprehensive Coverage: Maths chapter 14 class 8 solutions cover all topics and concepts related to factorization as per the Class 8 syllabus.

Step-by-Step Solutions: Class 8 maths ch 14 question answer are detailed, step-by-step explanations for each problem, making it easy for students to understand and apply mathematical concepts related to factorization.

Variety of Problems: A wide range of problems, including exercises and additional questions, to help students practice and test their understanding of factorization methods are discussed in ch 14 maths class 8.

## NCERT Solutions for Class 8 - Subject Wise

Factorization is a key skill to solve a problem where you need to find the value of x. It will strengthen your foundations of algebra, trigonometry, calculus, and higher class maths. It has a lot of applications like calculation, make multiplication easy, prime factorization, finding LCM and HCF, solving polynomial equations, quadratic equations, and simplifying expression, etc. In NCERT solutions for Class 8 Maths chapter 14 Factorizations, you will come across some applications like simplifying expressions and solving quadratic equations. Some important expressions from NCERT solutions for Class 8 Maths chapter 14 Factorizations are given below which you should remember.

• $a^{2}+2 a b+b^{2}=(a+b)^{2}$
• $a^{2}-2 a b+b^{2}=(a-b)^{2}$
• $a^{2}-b^{2}=(a+b)(a-b)$
• $x^{2}+(a+b) x+a b=(x+a)(x+b)$

## NCERT Books and NCERT Syllabus

### Frequently Asked Question (FAQs)

1. What are the important topics of Factorization ?

Factorization of algebraic expression, division of a monomial by another monomial, division of a polynomial by a monomial, and division of a polynomial by polynomial are covered in this chapter.

2. How many chapters are there in the CBSE class 8 maths ?

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

3. Does CBSE provide NCERT solution for class 8 ?

No, CBSE doesn't provide NCERT solutions for any class and subject.

4. Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

5. Where can I find the complete solutions of NCERT for class 8 maths ?

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

6. Which is the official website of NCERT ?

NCERT official is the official website of the NCERT where you can get NCERT textbooks and syllabus from class 1 to 12.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

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 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

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 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

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 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

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 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

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##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Finance Executive

A career as a Finance Executive requires one to be responsible for monitoring an organisation's income, investments and expenses to create and evaluate financial reports. His or her role involves performing audits, invoices, and budget preparations. He or she manages accounting activities, bank reconciliations, and payable and receivable accounts.

3 Jobs Available
##### Investment Banker

An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

3 Jobs Available
##### Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
##### Architect

Individuals in the architecture career are the building designers who plan the whole construction keeping the safety and requirements of the people. Individuals in architect career in India provides professional services for new constructions, alterations, renovations and several other activities. Individuals in architectural careers in India visit site locations to visualize their projects and prepare scaled drawings to submit to a client or employer as a design. Individuals in architecture careers also estimate build costs, materials needed, and the projected time frame to complete a build.

2 Jobs Available
##### Landscape Architect

Having a landscape architecture career, you are involved in site analysis, site inventory, land planning, planting design, grading, stormwater management, suitable design, and construction specification. Frederick Law Olmsted, the designer of Central Park in New York introduced the title “landscape architect”. The Australian Institute of Landscape Architects (AILA) proclaims that "Landscape Architects research, plan, design and advise on the stewardship, conservation and sustainability of development of the environment and spaces, both within and beyond the built environment". Therefore, individuals who opt for a career as a landscape architect are those who are educated and experienced in landscape architecture. Students need to pursue various landscape architecture degrees, such as M.Des, M.Plan to become landscape architects. If you have more questions regarding a career as a landscape architect or how to become a landscape architect then you can read the article to get your doubts cleared.

2 Jobs Available
##### Plumber

An expert in plumbing is aware of building regulations and safety standards and works to make sure these standards are upheld. Testing pipes for leakage using air pressure and other gauges, and also the ability to construct new pipe systems by cutting, fitting, measuring and threading pipes are some of the other more involved aspects of plumbing. Individuals in the plumber career path are self-employed or work for a small business employing less than ten people, though some might find working for larger entities or the government more desirable.

2 Jobs Available
##### Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

2 Jobs Available
##### Carpenter

Carpenters are typically construction workers. They stay involved in performing many types of construction activities. It includes cutting, fitting and assembling wood.  Carpenters may help in building constructions, bridges, big ships and boats. Here, in the article, we will discuss carpenter career path, carpenter salary, how to become a carpenter, carpenter job outlook.

2 Jobs Available
##### Welder

An individual who opts for a career as a welder is a professional tradesman who is skilled in creating a fusion between two metal pieces to join it together with the use of a manual or fully automatic welding machine in their welder career path. It is joined by intense heat and gas released between the metal pieces through the welding machine to permanently fix it.

2 Jobs Available
##### Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.

2 Jobs Available
##### Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
##### Veterinary Doctor

A veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.

5 Jobs Available
##### Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
##### Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.

4 Jobs Available
##### Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
##### Surgical Technologist

When it comes to an operation theatre, there are several tasks that are to be carried out before as well as after the operation or surgery has taken place. Such tasks are not possible without surgical tech and surgical tech tools. A single surgeon cannot do it all alone. It’s like for a footballer he needs his team’s support to score a goal the same goes for a surgeon. It is here, when a surgical technologist comes into the picture. It is the job of a surgical technologist to prepare the operation theatre with all the required equipment before the surgery. Not only that, once an operation is done it is the job of the surgical technologist to clean all the equipment. One has to fulfil the minimum requirements of surgical tech qualifications.

Also Read: Career as Nurse

3 Jobs Available
##### Maxillofacial Surgeon

A Maxillofacial Surgeon is a medical professional who performs facial surgeries that include tooth implant, neck, head or other surgeries such as removal of tumours, cosmetic surgeries and treatment of injuries on the face.

2 Jobs Available
##### Surgical Assistant

Surgical assistants are professionals in the service of saving others’ lives. They perform various medical procedures. In a career as a surgical assistant, one works in a team and contributes to the success of operations. Surgical assistants learn new procedures and update their knowledge of new medical technology and equipment. Surgical assistants clean and sterilize the tools used in surgery. In a career as a surgical assistant, individuals perform all the basic duties that allow surgeons to keep their focus on essential technical functions.

2 Jobs Available
##### Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.

4 Jobs Available
##### Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
##### Talent Agent

The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Talent Director

Individuals who opt for a career as a talent director are professionals who work in the entertainment industry. He or she is responsible for finding out the right talent through auditions for films, theatre productions, or shows. A talented director possesses strong knowledge of computer software used in filmmaking, CGI and animation. A talent acquisition director keeps himself or herself updated on various technical aspects such as lighting, camera angles and shots.

2 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Fashion Journalist

Fashion journalism involves performing research and writing about the most recent fashion trends. Journalists obtain this knowledge by collaborating with stylists, conducting interviews with fashion designers, and attending fashion shows, photoshoots, and conferences. A fashion Journalist  job is to write copy for trade and advertisement journals, fashion magazines, newspapers, and online fashion forums about style and fashion.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

Resource Links for Online MBA

3 Jobs Available
##### QA Manager

Quality Assurance Manager Job Description: A QA Manager is an administrative professional responsible for overseeing the activity of the QA department and staff. It involves developing, implementing and maintaining a system that is qualified and reliable for testing to meet specifications of products of organisations as well as development processes.

2 Jobs Available

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.

2 Jobs Available
##### Reliability Engineer

Are you searching for a Reliability Engineer job description? A Reliability Engineer is responsible for ensuring long lasting and high quality products. He or she ensures that materials, manufacturing equipment, components and processes are error free. A Reliability Engineer role comes with the responsibility of minimising risks and effectiveness of processes and equipment.

2 Jobs Available
##### Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Big Data Analytics Engineer

Big Data Analytics Engineer Job Description: A Big Data Analytics Engineer is responsible for collecting data from various sources. He or she has to sort the organised and chaotic data to find out patterns. The role of Big Data Engineer involves converting messy information into useful data that is clean, accurate and actionable.

2 Jobs Available
##### Cloud Solution Developer

A Cloud Solutions Developer is basically a Software Engineer with specialisation in cloud computing. He or she possesses a solid understanding of cloud systems including their operations, deployment with security and efficiency with no little downtime.

2 Jobs Available
##### CRM Technology Consultant

A Customer Relationship Management Technology Consultant or CRM Technology Consultant is responsible for monitoring and providing strategy for performance improvement with logged calls, performance metrics and revenue metrics. His or her role involves accessing data for team meetings, goal setting analytics as well as reporting to executives.

2 Jobs Available
##### IT Manager

Career as IT Manager  requires managing the various aspects of an organization's information technology systems. He or she is responsible for increasing productivity and solving problems related to software and hardware. While this role is typically one of the lower-level positions within an organisation, it comes with responsibilities related to people and ownership of systems.

2 Jobs Available