If $P(n)$ is a polynomial of degree $d$ then I have to show that there is a polynomial $h_p(x)$ of degree $\leq (d-1)$ such that $$\sum_{n\geq 0} P(n)x^{n} = \frac{h_p(x)}{(1-x)^{d+1}}.$$
I have no idea where to begin. There is a hint which says use the generating function for the polynomial. Now what is a generating function for any polynomial ? Any helpful thought on the problem will be highly appreciated. Thank you.