elementary number theory – Show that a prime p divides the sum of polynomials with integer coefficients of degree less than p – 1

Here’s the full question: Let $Finmathbb Z(x)$ be a polynomial of degree less than $p-1$, show that
$$
p | F(0) + F(1) + … + F(p-1)
$$

I don’t really know how I should get started with the problem, I’ve thought about Fermat’s little theorem but since $F$ is of degree less than $p-1$, it doesn’t really apply. Any hints on what theorems I should consider or approach to try would be great, thanks!