Exercise 10, § 6

Let $a \in \mathbf{A}$. For each polynomial $h \in \mathbf{A}[X]$ put $h_a(X) = h(X + a)$; show that $\operatorname{res}(f_a, g_a) = \operatorname{res}(f, g)$, $\operatorname{dis}(f_a) = \operatorname{dis}(f)$.