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