Inverse of polynomial over $\mathbb F_3$ finite field, quotient space A question about quotient spaces, something I do not fully understand yet, and can use some help.
$A = \mathbb F_3[x]$, $P = x^3-x+2\in A$
1) Show that $P$ is irreducible (I did it, it has no roots in $\mathbb F_3$).
2) Find the inverse of $x^2+P$ in $A/P$.
My problem is that I don't know what are the elements of $A/P$. I don't know what that is.
If I understand right, $x^2+P$ is the equivalence class of $x^2$ in $A/P$, but what now?

Hint: Try to find two polynomials S and T in $F_3[x]$ such that $S(x^3-x+2)+x^2T=1$.
What appens to this equality in $A/P$?
