I'm having trouble with this one, can anyone give me any hints?

Prove that if $\displaystyle a$ is any integer and the polynomial $\displaystyle f(x) = {x^{2} + ax + 1}$ factors (poly mod 9), then there are three distinct non-negative integers $\displaystyle y$ less than 9 such that $\displaystyle f(y)\equiv 0\bmod{9}$.