Answer
(a) $-1,2,\frac{1\pm\sqrt 3i}{2},-1\pm\sqrt 3i$
(b) $P(x)=(x-2)(x+1)(x+1+\sqrt 3i)(x+1-\sqrt 3i)(x-\frac{1+\sqrt 3i}{2})(x-\frac{1-\sqrt 3i}{2})$
Work Step by Step
(a) $P(x)=(x^3-8)(x^3+1)=(x-2)(x^2+2x+4)(x+1)(x^2-x+1)$
The zeros are $-1,2,\frac{1\pm\sqrt 3i}{2},-1\pm\sqrt 3i$
(b) $P(x)=(x-2)(x+1)(x+1+\sqrt 3i)(x+1-\sqrt 3i)(x-\frac{1+\sqrt 3i}{2})(x-\frac{1-\sqrt 3i}{2})$