MATHZ~ Factorise x^8 + 1

x8+1
= x8+2x4+1 - 2x4
= (x4+1)2 - [(√2)x2]2
= (x4 +√2 x2 +1)(x4 - √2 x2 +1)
consider the root of eqt x4 +√2 x2 +1 = 0 and x4 -√2 x2 +1 = 0
delta = 2 - 4 < 0
no real roots
.'. they can't be written as product of linear and quadratic factors with real coefficents.
the simplest form = (x4 +√2 x2 +1)(x4 - √2 x2 +1)