Okay, so textbook is incorrect. Thanks for clarifying!
:-D
But I still don't understand how synthetic division gave incorrect remainder? Doesn't the -2 at the end of your synthetic division represent the remainder?
-2 is the remainder for $g(x) = x^2 + \dfrac{x^2}{2} - 11x + 10 \, \text{ since }\, g\left(\frac{3}{2}\right) = -2$
$2 \cdot g(x) = f(x) \implies$ the remainder for g(x) is half that for f(x).
It's all a matter of which polynomial is used to determine the remainder ... I support -4 as the remainder since f(x) divided by (2x-3) was the original problem.