2009/021) Factorize the polynomial x^4 + 4 with real coefficient?

x^4 + 4
= x^4 + 4x^2 + 4 - 4x^2
= (x^2 + 2)^2 - (2x)^2
= (x^2 + 2x + 2) (x^2 - 2x + 2)