Answer
$x-\frac{1}{2}$ is a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(2x^4-x^3+2x-1)\div (x-\frac{1}{2})$
Rewrite as descending powers of $x$.
$(2x^4-x^3+0x^2+2x-1)\div (x-\frac{1}{2})$
The divisor is $x-\frac{1}{2}$, so the value of $c=\frac{1}{2}$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&--& --&& \\
\frac{1}{2}) &2&-1&0&2&-1 & &\\
& &1 &0 &0 &1& &\\
& -- & -- & --& -- &--&& \\
& 2 & 0& 0 &2 & 0&&\\
\end{matrix}$
The remainder is $0$.
Hence, $x-\frac{1}{2}$ is a factor of the given polynomial.
