Here is my problem:

Say if I have a irreducible polynomial for $\displaystyle GF(2^2)$ that is $\displaystyle x^2 + Nx + 1$, (N = elements of $\displaystyle GF(2)$) how do I determine the possible values of N ? Given the irreducible polynomial for $\displaystyle GF(2)$ is $\displaystyle x^2 + x + 1$

thanks alot!