Answer
Quotient = $\quad 5x^{2}-11$
Remainder = $\quad x+20$
Work Step by Step
$\begin{array}{llllll}
& 5x^{2} & & -11 & & \\
& -- & -- & -- & -- & \\
x^{2}+2 \ \ ) & 5x^{4} & & -x^{2} & +x & -2\\
& 5x^{4} & & +10x^{2} & & \\
& -- & -- & -- & -- & --\\
& & & -11x^{2} & +x & -2\\
& & & -11x^{2} & & -22\\
& & & -- & -- & --\\
& & & & +x & +20\\
& & & & &
\end{array}$
Check:
$(x^{2}+2)(5x^{2}-11)+(x+20)$
$=5x^{4}+10x^{2}-11x^{2}-22+x+20$
$=5x^{4}-x^{2}+x-2$
