# NCERT Solutions for Class 10 Maths Exercise 2.3

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NCERT solutions for Class 10 Maths Polynomials

## NCERT Solutions for Class 10 Maths Polynomials

1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.

(i),

(ii),

(iii),

Ans. (i)

Therefore, quotient = x – 3 and Remainder = 7x – 9

(ii)

Therefore, quotient = and, Remainder = 8

(iii)

Therefore, quotient = and, Remainder = −5x + 10

NCERT Solutions for Class 10 Maths Exercise 2.3

###### 2. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

(i)

(ii)

(iii)

Ans. (i)

Remainder = 0

Hence first polynomial is a factor of second polynomial.

(ii)

Remainder = 0

Hence first polynomial is a factor of second polynomial.

(iii)

Remainder ≠0

Hence first polynomial is not factor of second polynomial.

NCERT Solutions for Class 10 Maths Exercise 2.3

###### 3. Obtain all other zeroes of if two of its zeroes are and .

Ans. Two zeroes of are and which means that is a factor of .

Applying Division Algorithm to find more factors we get:

We have

= ()

= ()3

= 3()

= 3()(x+1)(x+1)

Therefore, other two zeroes of are −1 and −1.

NCERT Solutions for Class 10 Maths Exercise 2.3

###### 4. On dividing by a polynomial g(x), the quotient and remainder were (x-2) and (-2x+4) respectively. Find g(x).

Ans. Let, q(x) = (x – 2) and r(x) = (–2x+4)

According to Polynomial Division Algorithm, we have

p(x) = g(x).q(x) + r(x)

= g(x).(x−2)−2x+4

−4 = g(x).(x−2)

= g(x).(x−2)

g(x) =

So, Dividing by (x−2), we get

Therefore, we have g(x) =

NCERT Solutions for Class 10 Maths Exercise 2.3

###### 5. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

(i) deg p(x) = deg q(x)

(ii) deg q(x) = deg r(x)

(iii) deg r(x) = 0

Ans. (i) Let , g(x) = 3

So, we can see in this example that deg p(x) = deg q(x) = 2

(ii) Let and

We can see in this example that deg q(x) = deg r(x) = 1

(iii) Let, g(x) = x+3

We can see in this example that deg r(x) = 0

## NCERT Solutions for Class 10 Maths Exercise 2.3

NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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