Quotient Ring – Counting Elements in Z3[x]/?2x^3 + x + 1?

Question

How many elements are in the quotient ring $\displaystyle \frac{\mathbb Z_3[x]}{\langle 2x^3+ x+1\rangle}$ ?

I guess I should be using the division algorithm but I'm stuck on how to figure it out.

Answer 1

More generally, $$\left|\frac{\mathbb F_p[x]}{\text{ <an irreducible polynomial of degree $n$ over } \mathbb F_p>}\right|=p^n$$