There are 8 choices for the norm $\displaystyle \nu$ that make:

$\displaystyle r(y) = y^2 + y + \nu$ irreducible over $\displaystyle GF(2^4)$

why is this so??

this simple question (but hard for me) has been troubling me for weeks and no one can answer me why.

please help me with this

thank you very much