Answer
$x^2-7x+5$
Work Step by Step
Given \begin{equation}
\left(x^4-7 x^3+10 x^2-35 x+25\right) \div\left(x^2+5\right).
\end{equation} Use long division. $$
\begin{array}{r}
x^2-7x+5\phantom{)} \\
x^2+5{\overline{\smash{\big)}\,x^4-7x^3+10x^2-35x+25\phantom{)}}}\\
\underline{-~\phantom{(}(x^4+5x^2)\phantom{-b)}}\\
0-7x^3+5x^2-35x\phantom{)}\\
\underline{-~\phantom{()}(-7x^3-35x)}\\
0+5x^2+25\phantom{)}\\
\underline{-~\phantom{()}(5x^2+25)}\\
0\phantom{)}
\end{array}
$$ The solution is \begin{equation}
\frac{x^4-7 x^3+10 x^2-35 x+25}{x^2+5}= x^2-7x+5.
\end{equation}
