Answer
$5n^2+4n-8$
Work Step by Step
Given \begin{equation}
\left(5 n^4+19 n^3+14 n^2-16 n-16\right) \div\left(n^2+3n+2\right)
\end{equation} Use long division. $$
\begin{array}{r}
5n^2+4n-8\phantom{)} \\
n^2+3n+2{\overline{\smash{\big)}\,5n^4+19n^3+14n^2-16n-16\phantom{)}}}\\
\underline{-~\phantom{(}(5n^4+15n^3+10n^2)\phantom{-b)}}\\
0+4n^3+4n^2-16n\phantom{)}\\
\underline{-~\phantom{()}(4n^3+12n^2+8n)}\\
0-8n^2-24n-16\phantom{)}\\
\underline{-~\phantom{()}(-8n^2-24n-16)}\\
0\phantom{)}
\end{array}
$$The solution is
\begin{equation}
\frac{5n^4+19n^3+14n^2-16n-16}{n^2+3n+2}=5n^2+4n-8
\end{equation}
