Using the remainder theorem, find the remainder, when p(x) is div… - Vidyadip

Question

Using the remainder theorem, find the remainder, when $p(x)$ is divided by $g(x)$, where, $p(x)=2 x^3+x^2-15 x-12, g(x)=x+2$.

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Answer

$p(x)=2 x^3+x^2-15 x-12 g(x)=x+2$ by remainder theorem,
when $p(x)$ is divided by $(x+2)$,
then the remainder $=p(-2)$. Putting $x=-2$ in $p(x)$,
we get $p(-2)=(-2)^3+(-2)^2-15 \times(-2)-12=-16+4+30-12=6$
$\therefore$ Remainder $=6$
Thus, the remainder when $p(x)$ is divided by $g(x)$ is $6$ .

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