So, let $A=\mathbb{Z}/2\mathbb{Z}[X]$ and $ I=\{(X^2+X+1)P | P \in A \}$ I succeeded showing that this is the ideal, but now i have to find $A/I$, show that it have only 4 classes and find to what class corresponds elements like $X^3+X^2$ and $X^2+1$. I have some problems understanding the quotient groups. Mainly I considered looking at the wiki's page on quotients but there was sets and I arrived to the question.
It's very easy intuitevely follow that quotient is just mod n. But I dont understand the idea how to arrive to such result from having that $G/H=\{ xH | x \in G \}$.