Answer
$x^2+2x+5$
Work Step by Step
Given \begin{equation}
\left(x^4+2 x^3-10 x-25\right) \div\left(x^2-5\right)
\end{equation} Use long division. $$
\begin{array}{r}
x^2+2x+5\phantom{)} \\
x^2-5{\overline{\smash{\big)}\,x^4+2 x^3+0x^2-10 x-25\phantom{)}}}\\
\underline{-~\phantom{(}(x^4-5x^2)\phantom{-b)}}\\
0+2 x^3+5x^2-10x\phantom{)}\\
\underline{-~\phantom{()}(2x^3-10x)}\\
0+5x^2-25\phantom{)}\\
\underline{-~\phantom{()}(5x^2-25)}\\
0\phantom{)}
\end{array}
$$ The solution is \begin{equation}
\frac{x^4+2 x^3-10 x-25}{x^2-5}=x^2+2x+5
\end{equation}
