A fun question on polynomials

Here’s a somewhat basic but fun question on polynomials that I prepared for the Putnam seminar. I’ll post the solution by the end of this week.

Show that $x^4-200x^2+36$ and $x^4-240x^2+4$ are irreducible over $\mathbf{Q}$ , but reducible in $\mathbf{F}_p$ .

ErdosNinth