Chapter 2 Polynomials Ex 2.3

Question 1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by

(i) x + 1
(ii) x – 12
(iii) x
(iv) x + π
(v) 5 + 2x
Solution:
Let p (x) = x3 + 3x2 + 3x + 1
(i) The zero of x+ 1 is – 1. (∵ x+ 1 = 0= x = -1)

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 img 1

Question 2.
Find the remainder when x3-ax2 +6x-ais divided by x – a.
Solution:
The zero of x – a is a. (∵ x – a = 0 =» x= a)
Let p (x) = x3 – ax2 + 6x – a
So, p (a) = a3 – a (a)2 + 6a – a = a3 – a3 + 5a
⇒ p (a) = 5a
∴ Required remainder = 5a (By Remainder theorem)

Question 3.
Check whether 7 + 3x is a factor of 3x3+7x.

Solution:
Let f(x) = 3x3+7x
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 img 2