Answer
Quotient: $3x^{2}-7x+15$
Remainder: $-32$
Work Step by Step
$\begin{array}{llllll}
& 3x^{2} & -7x & +15 & & \\
& -- & -- & -- & -- & \\
x+2 \ \ ) & 3x^{3} & -x^{2} & +x & -2 & \\
& 3x^{3} & +6x^{2} & & & \\
& -- & -- & & & \\
& & -7x^{2} & +x & & \\
& & -7x & -14x & & \\
& & -- & -- & & \\
& & & 15x & -2 & \\
& & & 15x & +30 & \\
& & & -- & -- & \\
& & & & -32 & \\
& & & & &
\end{array}$
Check:
$(x+2)\left(3x^{2}-7x+15\right)+(-32)$
$=3x^{3}-7x^{2}+15x+6x^{2}-14x+30-32$
$=3x^{3}-x^{2}+x-2$
