suppose we have a polynomial P(x) where "a" is a root of multiplicity n. so we can write:
P(x)=(x-a)^n*Q(x) where Q is another polynomial. Suppose Q(a) is now zero, then (x-a) must be a factor of Q(x) as a is a root of Q(x), so we can write Q(x) = (x-a)*D(x) where D(x) is another polynomial. So...