Polynomial ring/Field/Zero/Linear factor/Fact

Let ${}K$ be a field and let ${}K[X]$ be the polynomial ring over ${}K$. Let ${}P\in K[X]$ be a polynomial and ${}a\in K$.

Then ${}a$ is a

zero

of ${}P$ if and only if ${}P$ is a multiple of the linear polynomial ${}X-a$.

Proof, Write another proof