Step 1

If \(x-\frac{1}{2}\) is a factor the the remainder when f(x) divided by it will be zero.

Put \(x-\frac{1}{2}=0\)

\(x=\frac{1}{2}\)

Step 2

Substitute \(x=\frac{1}{2}\) in f(x).

\(f(\frac{1}{2})=2(\frac{1}{2})^{4}-(\frac{1}{2})^{3}+2(\frac{1}{2})-1\)

\(=\frac{1}{8}-\frac{1}{8}+1-1\)

\(=0+0\)

\(=0\)

Thus the remainder is zero.

\(x-\frac{1}{2}\) is a factor of f(x)