Answer
$2x^{3}+2x-2$
Work Step by Step
Dividing with $x-c\displaystyle \qquad...\qquad c=\frac{1}{2}.$
Don't forget to place 0's for the missing terms.
$\begin{array}{rrrrrrrr}
\underline{\dfrac{1}{2}}\ | &2 & -1 & 2 & -3 & 1 & \\
& & 1 & 0 &1 & -1 & \\
& --& -- &-- &-- &-- & \\
&2 & 0 & 2 & -2 & 0 & \end{array}$
Quotient = $2x^{3}+2x-2$
Remainder = $0$
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{2x^{4}-x^{3}+2x^{2}-3x+1}{x-\frac{1}{2}}$ = $2x^{3}+2x-2$
