Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.
We have $p ( x )= x ^{3}+3 x ^{2}+3 x +1$ and $g ( x )= x +2$
$p (-2)=(-2)^{3}+3(-2)^{2}+3(-2)+1$
$=-8+3(4)+(-6)+1=-8+12-6+1$
$=-8-6+12+1=-14+13=-1$
$\therefore $ $p(-2) \neq 0$
Thus, $g(x)$ is not a factor of $p(x)$.
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