Answer
(a) $\pm1,\frac{1\pm\sqrt 3i}{2},\frac{-1\pm\sqrt 3i}{2}$
(b) $P(x)=(x+1)(x-1)(x-\frac{1+\sqrt 3i}{2})(x-\frac{1-\sqrt 3i}{2})(x+\frac{1-\sqrt 3i}{2})(x+\frac{1+\sqrt 3i}{2})$
Work Step by Step
$P(x)=x^6-1=(x^3+1)(x^3-1)=(x+1)(x^2-x+1)(x-1)(x^2+x+1)$
(a) Find the zeros for the quadratics, we have all the zeros as
$\pm1,\frac{1\pm\sqrt 3i}{2},\frac{-1\pm\sqrt 3i}{2}$
(b) $P(x)=(x+1)(x-1)(x-\frac{1+\sqrt 3i}{2})(x-\frac{1-\sqrt 3i}{2})(x+\frac{1-\sqrt 3i}{2})(x+\frac{1+\sqrt 3i}{2})$