Question Number 55070 by gunawan last updated on 17/Feb/19
$$\mathrm{Factorised}\:\mathrm{the}\:\mathrm{polynom}\:{z}^{\mathrm{4}} +\mathrm{1}\: \\ $$$$\mathrm{be}\:\mathrm{polynom}\:\mathrm{with}\:\mathrm{lower}\:\mathrm{degree}, \\ $$$$\mathrm{but}\:\mathrm{have}\:\mathrm{real}\:\mathrm{coefficient} \\ $$
Commented by mr W last updated on 17/Feb/19
$${z}^{\mathrm{4}} +\mathrm{1}=\left({z}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\left(\sqrt{\mathrm{2}}{z}\right)^{\mathrm{2}} \\ $$$$=\left({z}^{\mathrm{2}} +\sqrt{\mathrm{2}}{z}+\mathrm{1}\right)\left({z}^{\mathrm{2}} −\sqrt{\mathrm{2}}{z}+\mathrm{1}\right) \\ $$