Answer
$x^{4}-x^{2}+x+1+\displaystyle \frac{3}{x-2}$
Work Step by Step
Arrange the powers...
$(x^{5}-2x^{4}-x^{3}+3x^{2}-x+1)\div(x-2)$
(no missing powers)
$\begin{array}{lllllll}
\underline{2}| & 1 & -2 & -1 & 3 & -1 & 1\\
& & 2 & 0 & -2 & 2 & 2\\
& -- & -- & -- & -- & -- & --\\
& 1 & 0 & -1 & 1 & 1 & 3
\end{array}$
Result:
$=x^{4}-x^{2}+x+1+\displaystyle \frac{3}{x-2}$
