NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3

Question 1.
Find the remainder when x³ + 3x² + 3x + 1 is divided by
(i) x + 1
(ii) x – \(\frac { 1 }{ 2 }\)
(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)

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

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