A general Polynomial question,which needs to be proved

Let $P(x) = a_nx^n + ….. a_1x + a_0$

Let $g(x) = b_nx^n + ….. b_1x + b_0$

if $alpha$ is a common zero of the given two polynomials

prove that (P($alpha$)-g($alpha$)) is a factor of p(x)