Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}-4 x^{2}+x+6$, $g(x)=x-3$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}-4 x^{2}+x+6$, $g(x)=x-3$.
We have $p ( x )= x ^{3}-4 x ^{2}+ x +6$ and $g ( x )= x -3$
$ \therefore p (3) =(3)^{3}-4(3)^{2}+(3)+6=27-4(9)+3+6$
$=27-36+3+6=0 $
since $g(x)=0$
$\therefore g ( x )$ is a factor of $p ( x )$.
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