What is the Cardinality of this set? [closed]

This question was asked in my quiz in abstract algebra and I need help in solving it.

Let $\mathbb{F}_q$ be a finite field with q elements. Let $F= a_0 + ...+ a_{q-2} X^{q-2}\in \mathbb{F}_q[X]$ with degree F= q-2. Find the number of distinct zeroes of F in $\mathbb{F}_q$ , other that 0.

I have followed Field Theory from Artin's textbook but I am not able to have any intuition on how this question should be approached because coefficients of F themselves are variables.

Can you please which result should I use?

What can be said is that the zeros of the polynomial $X^q-1$ are exactly the nonzero elements of $\Bbb F_q$. Then $X^q-1 = (X-1)\cdot f$, where $f$ is a polynomial of degree $q-2$. The zeros of this polynomial are exactly the elements of $\Bbb F_q$ different from $0$ and $1$.