How to prove that polynomials of the form :
$P(x)= x^2+ax+a$ , where $a \in \mathbb{Z^{+}}$ \ $ \left \{ 4 \right \} $
are irreducible over ring $\mathbb{Z}$ of integers ?
Eisenstein's criterion and Cohn's criterion work fine for most of these polynomials but there are some exceptions that cannot be proved with these criterias such as irreducible polynomial:
$ x^2+36x+36$ or $ x^2+100x+100$ ,so I don't know how to prove that these exceptions are also irreducible polynomials .
I have checked statement above for many values of $a$ by small Maple program .