Johnny Kwong
Posted on Monday, 05 May, 2003 - 12:35 am:
Does anyone know how to factorise x6 +2 over the reals? I know it has no real roots so it must factorise into quadratics, but I got nowhere.

Please help
Michael DorÃ?©
Posted on Monday, 05 May, 2003 - 01:02 am:
Hint: first find its complex roots, then pair up these roots into conjugate pairs.
Demetres Christofides
Posted on Monday, 05 May, 2003 - 09:09 am:
Further hint: 6th roots of unity.

Demetres
Demetres Christofides
Posted on Tuesday, 06 May, 2003 - 08:53 am:
Maybe that was not helpful enough. The factorisation of x6 - 1 is
(x-1)(x-w)(x - w2)(x - w3)(x - w4)(x - w5)
where w = exp(2 pi/6)

Can you now factorise x6 + 2 over the complex numbers? Demetres