I have to demonstrate that "$\displaystyle P(x)$ is divisible by $\displaystyle (x-\alpha)$if and only if$\displaystyle p(\alpha)=0$."

My work : If $\displaystyle P(x)$ is divisible by $\displaystyle (x-\alpha)$, then I can write $\displaystyle P(x)=(x-\alpha)\cdot R(x)$.

If $\displaystyle P(\alpha)=0$, then $\displaystyle (\alpha-\alpha)\cdot R(\alpha)=0$, which is true. So $\displaystyle \Leftarrow$) is proved.

Now I have to show "if $\displaystyle P(x)$ is divisible by $\displaystyle (x-\alpha)$, then $\displaystyle P(\alpha)=0$." I don't know how to continue this.