Proposition 3

— Let $f$ be a non-zero element of $\mathbf{A}[X]$ and $a \in \mathbf{A}$. There exists just one integer $h \geq 0$ satisfying the conditions (i) and (ii) of Prop. 2. This is clear for condition (i), bearing in mind the fact that iff is divisible by $(X - \alpha)^h$, then $\deg f \geq h$ (IV, p. 9, Prop. 7).