Show that (x + 2) is a factor of f(x)

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Question:
Show that $(x+2)$ is a factor of $f(x)=x^{3}+4 x^{2}+x-6$

Solution:

Given: $f(x)=x^{3}+4 x^{2}+x-6$

Now, $f(-2)=(-2)^{3}+4(-2)^{2}+(-2)-6$

$=-8+16-2-6$

$=0$

$\therefore(x+2)$ is a factor of $f(x)=x^{3}+4 x^{2}+x-6$.

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