The remainder when $2x^3+3x^2-5x+7$ is divided by $(2x-1)$ is:

The divisor $2x-1$ vanishes at $x=1/2$, so the remainder is $p(1/2)=2(1/8)+3(1/4)-5(1/2)+7=1/4+3/4-5/2+7=11/2$. (Substituting $x=1$ instead of $x=1/2$ gives 7, and a sign slip on the $-5x$ term gives 21/2.)