# NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3.

• Polynomials Class 10 Ex 2.1
• Polynomials Class 10 Ex 2.2
• Polynomials Class 10 Ex 2.3
• Polynomials Class 10 Ex 2.4

## NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3

Ex 2.3 Class 10 Maths Question 1.
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
(i) p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2
(ii) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x
(iii) p(x) = x4– 5x + 6, g(x) = 2 – x2
Solution:

Ex 2.3 Class 10 Maths Question 2.
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
(i) t2 – 3, 2t4 + 3t3 – 2t2– 9t – 12
(ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2
(iii) x2 + 3x + 1, x5 – 4x+ x2 + 3x + 1
Solution:

∴  Remainder is 0, therefore, t2 – 3 is a factor of polynomial 2t4 + 3t3 – 2t2 -9t – 12.

∴ Remainder is 0, therefore, x2 + 3x + 1 is a factor of polynomial 3x4 + 5x3 – 7x2 + 2x + 2.

∴ Remainder = 2 ≠ 0, therefore, x3 – 3x + 1 is not a factor of polynomial x5 – 4x3 + x2+ 3x + 1.

Ex 2.3 Class 10 Maths Question 3.
Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are  and $\sqrt { \frac { 5 }{ 3 } }$ and –$\sqrt { \frac { 5 }{ 3 } }$
Solution:

$\frac { 1 }{ 3 }$ x (3x2– 5).Since both $\frac { 1 }{ 3 }$ and(3x2– 5)are the factors, therefore 3x2 – 5 is a factor of the given polynomial.
Now, we divide the given polynomial by 3x2 – 5.

Hence, the other zeroes of the given polynomial are -1 and –1.

Ex 2.3 Class 10 Maths Question 4.
On dividing x– 3x2 + x + 2bya polynomial g(x), the quotient and remainder were x – 2 and -2x + 4 respectively. Find g(x).
Solution:
x3 – 3x2 + x + 2  = g(x) x (x – 2) + (-2x + 4) [By division algorithm]

Ex 2.3 Class 10 Maths Question 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
Solution:
(i) p(x) = 2X2 + 2x + 8,
q(x) = x2 + x + 4,
g(x) = 2 and r(x) = 0

(ii) p(x) = x3 + x2 + x + 1,
q(x) = x + 1,
g(x) = x2 – 1 and r(x) = 2x + 2

(iii) p(x) = x3 – x2 + 2x + 3,
g(x) = x2 + 2,
q(x) = x – 1 and r(x) = 5

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