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NCERT exemplar Class 9 Maths solutions chapter 2 discusses polynomials, their properties, and solving polynomials for their zeroes. These NCERT exemplar Class 9 Maths chapter 2 solutions are designed by our subject-matter experts of mathematics. These solutions deliver accurate and elaborate answers to the questions of NCERT Class 9 Maths Book. These NCERT exemplar Class 9 Maths chapter 2 solutions build the concepts of polynomials by providing the students with a step-by-step approach. CBSE 9 maths Syllabus is followed for curating these NCERT exemplar Class 9 Maths solutions chapter 2.
Question:1
Which one of the following is a polynomial?
Answer:
Question:2
(A) 2
(B) 0
(C) 1
(D)
Answer:
[B]Question:3
Degree of the polynomial 4x^{4} + 0x^{3} + 0x^{5} + 5x + 7 is :
(A) 4
(B) 5
(C) 3
(D) 7
Answer:
[A]Question:4
Degree of the zero polynomial is
(A) 0
(B) 1
(C) Any natural number
(D) Not defined
Answer:
(D) Not definedQuestion:5
If , then is equal to
(A) 0
(B) 1
(C)
(D)
Answer:
(B) 1Question:6
The value of the polynomial 5x – 4x^{2} + 3 when x = – 1 is
(A) –6
(B) 6
(C) 2
(D) –2
Answer:
[A]Question:7
If , then is equal to
(A) 3 (B) 2x (C) 0 (D) 6
Answer:
(D) 6Question:8
Zero of the zero polynomial is
(A) 0
(B) 1
(C) Any real number
(D) Not define
Answer:
(C) Any real numberQuestion:9
Zero of the polynomial is
(A) (B) (C) (D)
Answer:
(B)Question:10
One of the zeroes of the polynomial is
(A) 2
(B)
(C)
(D) -2
Answer:
(B)Question:11
If is divided by x+1 , the remainder is
(A) 0
(B) 1
(C) 49
(D) 50
Answer:
(D) 50Question:12
If x+1 is a factor of the polynomial 2x^{2}+kx , then the value of k is
(A) –3 (B) 4 (C) 2 (D) –2
Answer:
(C) 2Question:13
x+1 is a factor of the polynomial
Answer:
(B)Question:14
One of the factors of is
(A) 5+x (B) 5-x (C) 5x-1 (D) 10x
Answer:
(D) 10xQuestion:15
The value of is
(A) (B) 477 (C) 487 (D) 497
Answer:
(D) 497Question:16
The factorization of is
(A)
(B)
(C)
(D)
Answer:
Let us factorize the given polynomialQuestion:17
Which of the following is a factor of
Answer:
(D) 3xyQuestion:18
The coefficient of x in the expansion of (x+3)^{3} is
(A) 1 (B) 9 (C) 18 (D) 27
Answer:
(D) 27Question:19
If the vlaue of is
(A) 1 (B) -1 (C)0 (D)
Answer:
(C) 0Question:20
Answer:
Given:Question:21
If , then is equal to
(A) 0 (B) abc (C) 3abc (D) 2abc
Answer:
(C) 3abcQuestion:1
Which of the following expressions are polynomials? Justify your answer
(i) 8
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
(i, ii, iv, vii)Question:2
Write whether the following statements are True or False. Justify your answer.
i. A binomial can have at most two terms
ii. Every polynomial is a binomial.
iii. A binomial may have degree 5.
iv. Zero of a polynomial is always 0
v.A polynomial cannot have more than one zero.
vi. The degree of the sum of two polynomials each of degree 5 is always 5
Answer:
i. FalseQuestion:1
Classify the following polynomials as polynomials in one variable, two variables etc.
(i)
(ii)
(iii)
(iv)
Answer:
(i) One VariableQuestion:2
Determine the degree of each of the following polynomials:
(i)
(ii)
(iii)
(iv)
Answer:
(i) OneQuestion:3
For the polynomial , write
(i) The degree of the polynomial
(ii) The coefficient of
(iii) The coefficient of
(iv) The constant term
Answer:
(i) 6Question:4
Write the coefficient of in each of the following
(i)
(ii)
(iii)
(iv)
Answer:
(i) 1Question:5
Classify the following as a constant, linear, quadratic and cubic polynomials:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
Answer:
(i) Cubic PolynomialQuestion:6
Give an example of a polynomial, which is:
(i) monomial of degree 1
(ii) binomial of degree 20
(iii) Trinomial of degree 2
Answer:
(i) xQuestion:7
Find the value of the polynomial , when x = 3 and also when x = – 3.
Answer:
[61, –143]Question:8
Answer:
Question:9
Find P(0), P(1), P(–2) for the following polynomials:
i.
ii.
Answer:
(i) P(0) = –3; P(1) = 3; P(–2) = –39P(0) = – 4; P(1) = – 3; P(–2) = 0
Solution.
Given polynomial is P(y) = (y + 2) (y – 2)
Put y = 0,
P(0)= (0 + 2) (0 – 2)
= (2) (–2)
= – 4
Put y = 1,
P(1) = (1 + 2) (1 – 2)
= (3) (–1)
= – 3
Put y = – 2,
P(–2) = (–2 + 2) (–2 – 2)
= (0) (–4)
= 0
Question:10
Verify whether the following are True or False :
i)-3 is a zero of x-3
ii) is a zero of
iii) is a zero of
iv) 0 and 2 are the zeroes of
v) –3 is a zero of
Answer:
i) FalseQuestion:11
Find the zeroes of the polynomial in each of the following :
i) p(x) = x - 4
ii) g(x) = 3 - 6x
iii)q(x) = 2x - 7
iv) h(y) = 2y
Answer:
i) 4Question:12
Find the zeroes of the polynomial :
Answer:
[0]Question:13
Answer:
QuotientQuestion:14
By Remainder Theorem find the remainder, when p(x) is divided by g(x) , where
Answer:
(i) 0Question:15
Check whether p(x) is multiple of g(x) or not
Answer:
(i) NoQuestion:16
Show that
(i) is a factor of
(ii) is a factor of
Answer:
(i) Here andQuestion:17
Determine which of the following polynomials has factor
(i)
(ii)
Answer:
(i) onlyQuestion:18
Show that p - 1 is a factor of p^{10} - 1 and also of p^{11} - 1 .
Answer:
To prove : Here we have to prove that is a factor of and also of .Question:19
For what value of m is divisible by ?
Answer:
m = 1Question:20
Answer:
Question:21
Find the value of m so that be a factor of .
Answer:
m=-2Question:22
If is a factor of , find the value of a.
Answer:
a = 2Question:23
Factorize :
(i)
(ii)
(iii)
(iv)
Answer:
Question:24
Answer:
Question:25
Using suitable identity, evaluate the following
Answer:
(i) 1092727Question:26
Answer:
Question:27
Answer:
Question:28
Answer:
(i)Question:29
Answer:
Question:30
Answer:
29Question:31
Answer:
Question:32
Answer:
(i)(1−4a)(1−4a)(1−4a)Question:34
Factorise:
(i)
(ii)
Answer:
(i)Question:35
Answer:
Question:36
Factorize
(i)
(ii)
Answer:
(i)Question:37
Without actually calculating the cubes, find the value of
(i)
(ii)
Answer:
(i)Question:38
Without finding the cubes, factorize
Answer:
Question:39
Find the value of
(i) when
(ii) when
Answer:
(i) 0Question:40
Give possible expressions for the length and breadth of the rectangle whose area is given by
Answer:
Length (2a+3)Question:1
Answer:
a = –1Question:2
Answer:
Value of a is 5Question:3
If both x – 2 and are factors of px^{2} + 5x + r, show that p = r.
Answer:
LetQuestion:4
Answer:
First of all, factorize x^{2} – 3x + 2Question:6
Answer:
Question:7
If a, b, c are all non-zero and a + b + c = 0, prove that
Answer:
Given,Question:8
If a + b + c = 5 and ab + bc + ca = 10, then prove that a^{3} + b^{3} + c^{3} –3abc = – 25
Answer:
Given: (a + b + c) = 5, ab + bc + ca = 10◊ Polynomial, monomial, and binomial as an algebraic expression.
◊ Degree of a polynomial: Maximum summation of exponents of variables in any term.
◊ Monomial and binomials: Expression of one-term and two-term, respectively.
◊ Coefficients of polynomials: The constant or number multiplied with variables in each term.
◊ Zeros of a polynomial of one variable: The value of a variable that will make polynomial zero value.
◊ Remainder theorem of polynomials; which will be the useful division of one polynomial by another
◊ Factor theorem of polynomials; we will use it to factorise the polynomials as a product of two or more than two polynomials of less degree.
◊ NCERT exemplar Class 9 Maths solutions chapter 2 includes applying identities for factorisation and division of polynomials and use of some algebraic identities.
These Class 9 Maths NCERT exemplar chapter 2 solutions will help the students understand the polynomials' concept and knowledge.
Polynomial is an algebraic expression of a single or many variables such that each term will have a different power of the variables.
These Class 9 Maths NCERT exemplar solutions chapter 2 Polynomials can be used strategically to learn and practice the concepts of polynomials and are appropriate to prepare a student to take on other books such as NCERT Class 9 Maths, RD Sharma Class 9 Maths or RS Aggarwal Class 9 Maths.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
A student can always solve the zeros of a polynomial with degree 2. It is known as the quadratic equation. Sometimes we can solve cubic equations or zeros of higher degree polynomials. With the help of a computer, we can draw the graph of a polynomial of any degree and then locate it's zero.
NCERT exemplar Class 9 Maths solutions chapter 2 states that it is the expansion of the nth power of any binomial such as (a+b)2; this is also known as a binomial theorem.
In an equation, two expressions are equated, whereas expression is the mathematical representation of different terms of any variable.
A clear understanding of Polynomials can prepare a student to solve problems based on Algebra, which ranges up to 3% of the whole paper.
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