The first part of my question asked : State all the irreducible Polynomials in $\mathbb{Z}_2[x]$ of order 3.
I was able to do this and get the following polynomials :
$x^3 + x^2 + x + 1 \Rightarrow$ reducible
$x^3 + x^2 + 1 \Rightarrow$ irreducible
$x^3 + x + 1 \Rightarrow$ irreducible
$x^3 + 1 \Rightarrow$ reducible
and the other polynomials in $\mathbb{Z}_2[x]$ are trivially reducible.
I set $f=x^3 + x^2 + 1$, $g=x^3 + x + 1$.
I then have to take $\mathbb{Z}_2[x]/f$ and $\mathbb{Z}_2[x]/g$ and construct an isomorphism between the two.
My real problem is understanding what these two fields $\mathbb{Z}_2[x]/f$ and $\mathbb{Z}_2[x]/g$ really are- and how I can build an isomorphism between them.
If anyone could help I'd be very grateful :)