Given , and , factorize as a product of real quadratic polynomials.
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Given $a, \theta \in \mathbb R, m \in \mathbb N$, and $P(x) = x^{2m}- 2|a|^mx^m \cos \theta +a^{2m}$, factorize $P(x)$ as a product of $m$ real quadratic polynomials.
Source: Međunarodna matematička olimpijada, shortlist 1973
Školjka 
, and 
, factorize 
as a product of 
real quadratic polynomials.