Answer
$P(a)=18$
Work Step by Step
Using the synthetic division shown below, the remainder (bottom-right number) of $(
x^3+4x^2-8x-6
)\div(
x+2
),$ is
\begin{align*}
18
.\end{align*}
Substituting $x=
-2
$ in $P(x)=
x^3+4x^2-8x-6
,$ then by the Remainder Theorem, the remainder when $P(x)$ is divided by $
x+2
$ is
\begin{align*}
P(-2)&=
(-2)^3+4(-2)^2-8(-2)-6
\\&=
-8+4(4)-8(-2)-6
\\&=
-8+16+16-6
\\&=
18
.\end{align*}
The two solutions above show that the remainder, $P(a),$ is
\begin{align*}
P(a)=18
.\end{align*}
