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

Using the division algorithm, you can show that each element in the quotient ring is represented by a unique polynomial in $\mathbb{Z}_3[x]$ of degree $\leq 2$. How many such polynomials are there?
It's exactly like counting the number of elements of $\mathbb{Z}/n\mathbb{Z}$.
