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