Factor x6−7x3+6x^6 - 7x^3 + 6x6−7x3+6 completely over the reals.
(x−1)(x2+x+1)(x3−6)(x-1)(x^2+x+1)(x^3-6)(x−1)(x2+x+1)(x3−6)
(x3−1)(x3−6)(x^3-1)(x^3-6)(x3−1)(x3−6)
(x3−1)(x−63)(x2+x63+363)(x^3-1)(x-\sqrt[3]{6})(x^2 + x\sqrt[3]{6} + \sqrt[3]{36})(x3−1)(x−36)(x2+x36+336)
Cannot be factored over the reals