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Question

Which of the following is/are true?

A
x+2 is a factor of x3+3x2+5x+6
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B
x+2 is not a factor of x3+3x2+5x+6
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C
x+2 is not a factor of 2x+4
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D
x+2 is a factor of 2x+4
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Solution

The correct option is D x+2 is a factor of 2x+4
Factor theorem states if p(x) is a polynomial of degree n1 and a is any real number then xa is a factor of p(x), if and only if p(a)=0

The zero of x+2 is 2.
Let p(x)=x3+3x2+5x+6 and s(x)=2x+4

Then, p(2)=(2)3+3(2)2+5(2)+6
=8+1210+6=0
So, by the Factor Theorem, x+2 is a factor of x3+3x2+5x+6.

Again, s(2)=2(2)+4=0
So, x+2 is a factor of 2x+4.

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