$I=\langle x^2,2x,4\rangle$ is an ideal of $\Bbb Z[x]$.
Prove that $I$ is not a principal ideal and find the size of $\Bbb Z[x]/I$.
Using the theorem that ideals are principal iff the generator is irreducible, I think the first part is obvious since $x^2$ is reduced to x(x). I'm slightly thrown by having multiple elements in the generator in this case, so if that complicates things I'd love a heads up.
Mostly I'm confused about finding the size of $\Bbb Z[x]/I$. Noting that $\pi:Z[x]\rightarrow Z[x]/I$ is the canonical homomorphism and it maps $f(x)\mapsto f(x)+I$...but I have no clue how to find the size of this...