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Question

For the polynomial f(x)=x36x2+11x6, which of the following is/are true?
(Check using Remainder Theorem)

A
On dividing f(x) by x+1, the remainder obtained is 24
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B
On dividing f(x) by x2, the remainder obtained is 0
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C
On dividing f(x) by x2, the remainder obtained is 1
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D
All of the above
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Solution

The correct option is B On dividing f(x) by x2, the remainder obtained is 0
The given polynomial is f(x)=x36x2+11x6.

Remainder Theorem states that if a polynomial p(x) is divided by xa, then the remainder obtained is p(a)

On dividing f(x) by x2, the remainder obtained will be:
f(2)=236(2)2+11(2)6=824+226=0

and
On dividing f(x) by x+1, the remainder obtained will be:
f(1)=(1)36(1)2+11(1)6=16116=24


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