NCERT Solutions for Exercise 2.3 Class 10 Maths Chapter 2 - Polynomials

# NCERT Solutions for Exercise 2.3 Class 10 Maths Chapter 2 - Polynomials

Edited By Ramraj Saini | Updated on Nov 08, 2023 06:31 PM IST | #CBSE Class 10th

## NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.3 Polynomials

NCERT Solutions for class 10 maths ex 2.3 Polynomials is discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Exercise 2.3 of Class 10 Maths introduces the notion of polynomials in x with real coefficients, the notion of polynomials of degrees 1, 2, 3, quadratic equation, and many more with numerical problems on the Polynomials chapter.

The Class 10th Maths chapter 2 exercise 2.3 moves towards the topics like the class of addition, subtraction and multiplication of polynomials. Also, zeroes/roots of a polynomial function f(x). Also students can find all exercise listed below, practice them to command the maths concepts.

## Access Exercise 2.3 Class 10 Maths Answers

Polynomials Class 10 Maths Chapter 2 Excercise: 2.3

Answer: The polynomial division is carried out as follows

The quotient is x-3 and the remainder is 7x-9

The division is carried out as follows

The quotient is $x^2+x-3$

and the remainder is 8

Answer: The polynomial is divided as follows

The quotient is $-x^2-2$ and the remainder is $-5x+10$

$t^2 - 3, 2t^4 + 3t^3 - 2t^2 - 9t - 12$

After dividing we got the remainder as zero. So $t^2 - 3$ is a factor of $2t^4 + 3t^3 - 2t^2 - 9t - 12$

$x^2 + 3x + 1, 3x^4 + 5x^3 - 7x^2 + 2x + 2$

Answer: To check whether the first polynomial is a factor of the second polynomial we have to get the remainder as zero after the division

After division, the remainder is zero thus $x^2+3x+1$ is a factor of $3x^4 + 5x^3 - 7x^2 + 2x + 2$

Q2 (3) Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $x^3 - 3x + 1, x^5 - 4x^3 + x^2 + 3x + 1$

Answer: The polynomial division is carried out as follows

The remainder is not zero, there for the first polynomial is not a factor of the second polynomial

Q3 Obtain all other zeroes of $3x^4 + 6x^3 - 2x^2 - 10x - 5$ , if two of its zeroes are $\sqrt {\frac{{ 5 }}{3}} \: \:and \: \: - \sqrt {\frac{5}{3}}$

Two of the zeroes of the given polynomial are $\sqrt {\frac{{ 5 }}{3}} \: \:and \: \: - \sqrt {\frac{5}{3}}$ .

Therefore two of the factors of the given polynomial are $x-\sqrt{\frac{5}{3}}$ and $x+\sqrt{\frac{5}{3}}$

$(x+\sqrt{\frac{5}{3}})\times (x-\sqrt{\frac{5}{3}})=x^{2}-\frac{5}{3}$

$x^{2}-\frac{5}{3}$ is a factor of the given polynomial.

To find the other factors we divide the given polynomial with $3\times (x^{2}-\frac{5}{3})=3x^{2}-5$

The quotient we have obtained after performing the division is $x^{2}+2x+1$

$\\x^{2}+2x+1\\ =x^{2}+x+x+1\\ =x(x+1)+(x+1)\\ =(x+1)^{2}$

(x+1) 2 = 0

x = -1

The other two zeroes of the given polynomial are -1.

remainder =-2x+4

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

Carrying out the polynomial division as follows

$g(x)={x^2-x+1}$

Answer: deg p(x) will be equal to the degree of q(x) if the divisor is a constant. For example

$\\p(x)=2x^2-2x+8\\q(x)=x^2-x+4\\g(x)=2\\r(x)=0$

Answer: Example for a polynomial with deg q(x) = deg r(x) is given below

example for the polynomial which satisfies the division algorithm with r(x)=0 is given below

$\\p(x)=x^3+3x^2+3x+5\\q(x)=x^2+2x+1\\g(x)=x+1\\r(x)=4$

## More About NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.3

The problems from the concepts of division of polynomial p(x) with polynomial g(x) are covered in exercise 2.3 Class 10 Maths. The Introductory numerical questions of NCERT solutions for Class 10 Maths chapter 2 exercise 2.3 is to represent the numerical problems of finding quotient and remainder. And later on questions of Class 10 Maths chapter 2 exercise 2.3 is to find the polynomial if Quotient and remainder is given.

Also Read| Polynomials Class 10 Notes

## Key Features of NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.3

• The solved example before the exercise 2.3 Class 10 Maths and the NCERT solutions for Class 10 Maths chapter 2 exercise 2.3 are important as it covers questions from the basic division of Polynomials

• If students can solve each and every question of this exercise 2.3 Class 10 Maths he will be able to grasp the factorization concept of the polynomial as given in Class 10th Maths chapter 2 exercise 2.4

• For Class 10 final exams students may get a short answer or long answer questions from the type covered in the Class 10 Maths chapter 2 exercise 2.3

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## NCERT Solutions of Class 10 Subject Wise

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As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

## Subject Wise NCERT Exemplar Solutions

1. Define Polynomial?

Polynomial '' comes from the word ‘Poly’ (Meaning Many) and ‘nomial’ (in this case meaning Term)-so it means many terms.

2. Can a in polynomial ax² + bx + c be equal to zero?

No, a ≠ 0 because it will turn into a linear equation

3. What happens when zeroes of quadratic equation are equal?

When ax² + bx + c =0 has roots/zeros  α and β if they are equal, then sign of  a (coef of  x²) and c (constant term) must be equal

4. What is the formula of sum of roots of Polynomial ax² + bx + c =0?

sum of roots = α + β = -(b/a).

5. What is the formula of Product of roots of Polynomial ax² + bx + c =0?

Product of roots = α * β = (c/a)

6. What does a polynomial with degree = 3 called?

A polynomial with degree  = 3 is called Cubic  polynomial

7. What is division algorithm in Polynomial?

Ans Consider the functions,  f(x) and g(x) are any two polynomials with for any value of x, g(x) ≠ 0, then we have derived an expression-
f(x) = g(x) × q(x) + r(x)
Dividend = Divisor * Quotient + Remainder

8. What happens when a polynomial is multiplied by itself?

Each term of the first polynomial is multiplied by each term of the second polynomial when the two polynomials are multiplied.

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### Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?

Hello

The Sadhu Ashram in Aligarh is located in Chhalesar . The ashram is open every day of the week, except for Thursdays . On Mondays, Wednesdays, and Saturdays, it's open from 8:00 a.m. to 7:30 p.m., while on Tuesdays and Fridays, it's open from 7:30 a.m. to 7:30 p.m. and 7:30 a.m. to 6:00 a.m., respectively . Sundays have varying hours from 7:00 a.m. to 8:30 p.m. . You can find it at Chhalesar, Aligarh - 202127 .

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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