Answer
$3x^2+5$
Work Step by Step
Given \begin{equation}
\left(3 x^3+5 x^2+6 x+10\right) \div\left(x^2+2\right)
\end{equation} Use long division.
$$
\begin{array}{r}
3x+5\phantom{)} \\
x^2+2{\overline{\smash{\big)}\,3 x^3+5 x^2+6 x+10\phantom{)}}}\\
\underline{-~\phantom{(}(3x^3+6x)\phantom{-b)}}\\
0+5x^2+10\phantom{)}\\
\underline{-~\phantom{()}(5x^2+10)}\\
0\phantom{)}
\end{array} $$ The solution is
\begin{equation}
\frac{3 x^3+5 x^2+6 x+10}{x^2+2}=3x^2+5
\end{equation}
