Why $f(0)\neq 0$ where $f $ is a polynomial over the field $\mathbb F_q$ and $\deg(f)=m > 0$?

Question

To construct the residue class ring $\mathbb F_q[x]/(f)$ having $q^m-1$ non-zero elements is it necessary for $f(0) \neq 0$? Why or why not?

I have worked with different examples such as $x^3+x=f \in F_2[x]$ but could not find why $f(0) \neq 0$ is necessary for residue class ring $F_q[x]/(f)$.