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

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

Any element of this quotient ring is of the form $a_0+a_1x+a_2x^2+\langle 2x^3+x+1\rangle $ where $a_i\in \mathbb Z_3$

Thus we have $27$ elements

Note:whenever there is a polynomial $f(x)$ of degree $\geq 3 \in \mathbb Z_3[x]$ then by division algorithm we will get two polynomials $q(x),r(x)$ such that $f(x)=(2x^3+x+1)q(x)+r(x) $ where $r(x)=0 $ or $\deg r(x)<\deg (2x^3+x+1)$ which is $2$