**NCERT Solutions for Class
9 Maths Chapter 2 Polynomials Ex 2.3**

NCERT Solutions for Class
9 Maths Chapter 2 Polynomials Ex 2.3 are the part of NCERT Solutions for Class
9 Maths. Here you can find the NCERT Solutions for Class 9 Maths Chapter 2
Polynomials Ex 2.3.

**NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.1****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.2****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.3****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.4****NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.5**

**Ex
2.3 Class 9 Maths** **Question 1.****
**Find the remainder when x

^{3}+ 3x

^{2}+ 3x + 1 is divided by

**(i)**x + 1

**(ii)**x – ½

**(iii)**x

**(iv)**x + Ï€

**(v)**5 + 2x

**Solution:****
**Let p(x) = x

^{3}+ 3x

^{2}+ 3x + 1

**(i)**The zero of x + 1 is -1.

∴ p(-1) = (-1)

^{3}+ 3(-1)

^{2}+ 3(-1) + 1

= -1 + 3 – 3 + 1 = 0

Thus, the required remainder = 0

**(ii)** The zero of x – ½ is ½.

Thus, the required remainder = 27/8

**(iii)**
The zero of x is 0.

∴ p(0) = (0)^{3} + 3(0)^{2} + 3(0) + 1

= 0 + 0 + 0 + 1 = 1

Thus, the required remainder = 1.

**(iv)**
The zero of x + Ï€ is -Ï€.

p(-Ï€) = (-Ï€)^{3} + 3(-Ï€)^{2} + 3(-Ï€) + 1

= -Ï€^{3} + 3Ï€^{2} +
(-3Ï€) + 1

= -Ï€^{3} + 3Ï€^{2} –
3Ï€ + 1

Thus, the required remainder is -Ï€^{3} + 3Ï€^{2} – 3Ï€ +
1.

**(v)** The zero of 5 + 2x is −5/2.

Thus, the required remainder is −27/8.

**Ex 2.3 Class 9 Maths** **Question 2.**

Find the remainder when x^{3} – ax^{2} +
6x – a is divided by x – a.

**Solution:
**We have, p(x) = x

^{3}– ax

^{2}+ 6x – a and zero of x – a is a.

∴ p(a) = (a)

^{3}– a(a)

^{2}+ 6(a) – a

= a

^{3}– a

^{3}+ 6a – a = 5a

Thus, the required remainder is 5a.

**Ex
2.3 Class 9 Maths** **Question 3.**

Check
whether 7 + 3x is a factor of 3x^{3 }+ 7x.

**Solution:****
**We have, p(x) = 3x

^{3 }+ 7x and zero of 7 + 3x is −7/3.

Since, (−490/9) ≠ 0, i.e. the remainder is not 0.

∴ 3x

^{3}+ 7x is not divisible by 7 + 3x.

Thus, 7 + 3x is not a factor of 3x

^{3}+ 7x.

**NCERT Solutions for Maths Class 10**