Answer
Quotient = $\quad 2x^{2}$
Remainder = $\quad -x^{2}+x+1$
Work Step by Step
$\begin{array}{lllllll}
& 2x^{2} & & & & & \\
& -- & -- & -- & -- & & \\
2x^{3}-1 \ \ ) & 4x^{5} & +0 & +0 & -3x^{2} & +x & +1\\
& 4x^{5} & & & -2x^{2} & & \\
& -- & -- & -- & -- & -- & --\\
& & & & -x^{2} & +x & +1\\
& & & & & & \\
& & & & & &
\end{array}$
Check:
$(2x^{3}-1)(2x^{2})+(-x^{2}+x+1)$
$=4x^{5}-2x^{2}-x^{2}+x+1$
$=4x^{5}-3x^{2}+x+1$
