Let $T$ be a non-zero shift-invariant endomorphism of $\mathbb{K}[X]$, and let $n(T)$ be the natural number such that $\deg(Tp) = \max\{-1, \deg(p) - n(T)\}$ for every $p \in \mathbb{K}[X]$. Deduce $\ker(T)$ in terms of $n(T)$.
Let $T$ be a non-zero shift-invariant endomorphism of $\mathbb{K}[X]$, and let $n(T)$ be the natural number such that $\deg(Tp) = \max\{-1, \deg(p) - n(T)\}$ for every $p \in \mathbb{K}[X]$.
Deduce $\ker(T)$ in terms of $n(T)$.