Prove the factorization of a polynomial over $(\Bbb Z/p\Bbb Z)[X]$

Question

Let $f(x) = x^4 -10x^2 + 1$ a polynomial. Prove that $f$ has a factorization over $(\Bbb Z/p\Bbb Z)[X]$, $\forall$p prime number.

I have proved that this polynomial is irreducible over $\Bbb Z[X]$ using rational root theorem, but factor over $(\Bbb Z/2\Bbb Z)[X]$ because of $\overline 1$ is a root.

Now I'm not able to prove the generalization.