IMO 1973 — Shortlisted problems Question 16

(CUB 2) Given $a,\theta\in\mathbb R$, $m\in\mathbb N$, and $P(x)=x^{2m}-2|a|^m x^m\cos\theta+a^{2m}$, factorize $P(x)$ as a product of $m$ real quadratic polynomials.