## Chapter 2 Polynomials Ex 2.3

**Question 1.Find the remainder when x ^{3} + 3x^{2} + 3x + 1 is divided by**

**(i) x + 1**

**(ii) x –**12

**(iii) x**

**(iv) x + π**

**(v) 5 + 2x**

Solution:

Let p (x) = x

Solution:

^{3}+ 3x

^{2}+ 3x + 1

(i) The zero of x+ 1 is – 1. (∵ x+ 1 = 0= x = -1)

**Question 2.Find the remainder when x ^{3}-ax^{2} +6x-ais divided by x – a.Solution:** The zero of x – a is a. (∵ x – a = 0 =» x= a)

Let p (x) = x

^{3}– ax

^{2}+ 6x – a

So, p (a) = a

^{3}– a (a)

^{2}+ 6a – a = a

^{3}– a

^{3}+ 5a

⇒ p (a) = 5a

∴ Required remainder = 5a (By Remainder theorem)

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

^{}

**Solution:**

Let f(x) = 3x

^{3}+7x