Originally Posted by

**chadlyter** I am trying to prove the following and don't even know where to get started:

f(x) = as sub n x^n+ a sub n-1 + ....+a0

f'(x) is n a sub n x ^ n-1 + (n-1) a sub n-1 x^n-2+...+a1. If u belongs to N and (x-c)^u divides f(x) but (x-c)^u-1 does not we can say that c is a root of f (x) multiplicity u

Now suppose c is a root of f (x) of multiplicity u greater than 1. Prove that c is a root of f'(x) as well and suppose c is root of both f (x) and conversely c is a root of f (x) of multiplicity u greater than 1.