I have the polynomial $\displaystyle f(x) = x^4-10x^2+1 $ over $\displaystyle \mathbb Q $. It can be easily seen that Klein's Four group is the Galois group of this polynomial.

How can I show that the corresponding polynomial

$\displaystyle g(x) \in \mathbb F_p[x] $ is irreducible in $\displaystyle \mathbb F_p[x] $ for every prime $\displaystyle p $.