Answer
no, $x=-2$ is NOT a solution
Work Step by Step
Using the Remainder Theorem, the remainder when $P(x)=
3x^3+10x^2+3x-9
,$ is divided by $(
x+2
)$ is given by $
P(-2)
$.
Substituting $x=-2$ in the function above results to
\begin{align*}
P(-2)&=
3(-2)^3+10(-2)^2+3(-2)-9
\\&=
3(-8)+10(4)+3(-2)-9
\\&=
-24+40-6-9
\\&=
1
.\end{align*}
Since the remainder (equal to $
1
)$ is not zero, then $(
x+2
)$ DOES NOT evenly divide $P(x)$. Hence, $
x=-2
$ is NOT a solution of $
3x^3+10x^2+3x-9=0
$.
