Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 2 / 17F / ii

The cyclotomic polynomial is ${\Phi }_8(t)=t^4+1$. Over ${\mathbb{F}}_7$,since the middle coefficient in the product is $2-9=-7=0$. Both factors have positive degree, proving reducibility. In fact their discriminant $5$ is not a square modulo $7$, so these are the two irreducible quadratic factors.