I'm having troubles with this problem

Let $\displaystyle F$ be a Field, and suppose that $\displaystyle a\in F$ and $\displaystyle f(x)\in F[x]$. Show $\displaystyle f(a) $ is the remainder when $\displaystyle f(x)$ is divided by $\displaystyle x-a $

The case when $\displaystyle f(a)=0 $ is trivial but I don't know what to do from there.