Theorem

Let $\mathbb{F}$ be a field and suppose we have $a,b\in\mathbb{F}[x]$ with $b\not=0$. Then, $\exists q,r\in\mathbb{F}[x]$ s.t. $$a=bq+r$$with either $r=0$ or $r\not=0$ and $\deg r<\deg b$.

Remark

Analogue to Euclidean Algorithm.