Answer
Quotient $Q(x)=x^3-5x^2+17x-83$ Remainder $R(x)=422$
Work Step by Step
$\frac{x^4-8x^2+2x+7}{x+5}$, dividing using synthetic division:
$\begin{array}{lllll}
\underline{-5}| &1& 0 & -8 & 2& 7 & \\
& & -5&25&-85 &415 & \\
\hline & & & & \\
&1& -5 & 17 & -83&422 &
\end{array}$
$(x^4-8x^2+2x+7)\div(x+5)=x^3-5x^2+17x-83$ $+\frac{422}{x+5}$.
thus, Quotient is $Q(x)=x^3-5x^2+17x-83$ and remainder is $R(x)=422$
