Answer
$2x^{4}-7x^{3}+15x^{2}-31x+64-\displaystyle \frac{129}{x+2}$
Work Step by Step
Dividing with $x-c\qquad...\qquad c=-2.$
$\begin{array}{rrrrrrrr}
\underline{-2}| &2 & -3& 1 & -1 & 2 & -1 & & \\
& & -4 & 14 & -30 & 62 & -128 & & \\
& --& -- &-- &-- &-- & -- & & \\
&2 & -7 & 15 & -31 & 64 & -129 & & \end{array}$
Quotient = $ 2x^{4}-7x^{3}+15x^{2}-31x+64$
Remainder = $-129$
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{2x^{5}-3x^{4}+x^{3}-x^{2}+2x-1}{x+2}$ = $2x^{4}-7x^{3}+15x^{2}-31x+64-\displaystyle \frac{129}{x+2}$
