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Question

Examine whether x + 2 is a factor of x3+3x2+5x+6 and 2x + 4.

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Solution

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 + 12 - 10 + 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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