EDB — 1SK

[1SK] Prerequisites:[19M]↺↻, [1SF]↺↻.

Fix $𝜃,𝜏\in ℂ$ with $𝜃\ne 𝜏$, $q(x)$ a polynomial, and $k\in \mathbb{N}$. Let’s define $p(x)=(x-𝜃{)}^k$. Show that

if and only if

with $r$ polynomial of degree at most $k-1$ and $\tilde{q}$ polynomial of the same degree as $q$.