Examples for Remainder Theorem

Example 1: Find the remainder when x4 + x3 – 2x2 + x + 1 is divided by x – 1.

Solution : Here, p(x) = x4 + x3 – 2x2 + x + 1, and the zero of x – 1 is 1.

So, p(1) = (1)4 + (1)3 – 2(1)2 + 1 + 1

= 2

So, by the Remainder Theorem, 2 is the remainder when x4 + x3 – 2x2 + x + 1 is divided by x – 1.


Example 2: Check whether the polynomial q(t) = 4t3 + 4t2– t – 1 is a multiple of 2t + 1.

Solution : As you know, q(t) will be a multiple of 2t + 1 only, if 2t + 1 divides q(t) leaving remainder zero. Now, taking 2t + 1 = 0, we have t = –1 /2.

Also,

q(-1 /2) = 4(-1 /2) 3 + 4(-1 /2) 2– (-1 /2)  – 1

= –1 /2 + 1 + 1 /2 – 1

= 0

So the remainder obtained on dividing q(t) by 2t + 1 is 0.

So, 2t + 1 is a factor of the given polynomial q(t), that is q(t) is a multiple of 2t + 1.


 

One thought on “Examples for Remainder Theorem

Comments are closed.