Showing $x^4-16x^2+4$ is irreducible over $\mathbb{Q}$
Is there a slick way to do this? I mean first we could perhaps show it has no roots in $\mathbb{Q}$ by substituting dummy variable $t$ and solving $t^2-16t+4=0$, and then show that it doesn't factor as two quadratics by trying to match coefficients. Is there a better way to do this?