Show that for some polynomial g(x) with integer coefficients.
First note that x = 1 is a root of f(x) and so x - 1 is a factor of f(x). Then .
Now note that x = 1 is also a root of f'(x). Then x - 1 is a factor of .
It follows that (x - 1) is a factor of h(x). Therefore and the result follows.