Answer
$\frac{4 a^3+2 a+40}{a+2}=4a^2-8a+18+\frac{4}{a+2}$
Work Step by Step
Given \begin{equation}
\begin{aligned}
\left(4 a^3+2 a+40\right) \div(a+2).
\end{aligned}
\end{equation} Use synthetic division. \begin{equation}
\begin{array}{r|rrrr}
-2&4 & 0 & 2 &40 \\
& & -8 & 16& -36 \\
\hline &4 & -8 & 18 & -4
\end{array}
\end{equation} The solution is \begin{equation}
\begin{aligned}
\frac{4 a^3+2 a+40}{a+2}=4a^2-8a+18+\frac{4}{a+2}.
\end{aligned}
\end{equation}
