Answer
a) The zeros of the function are: $\{2,-1+\sqrt 3i, -1-\sqrt 3i\}$
b) $P(x)=(x-2)(x^{2}+2x+4)$
Work Step by Step
(a) Zeros
Factor the polynomial completely to obtain:
$P(x)=x^{3}-8=(x-2)(x^{2}+2x+4)$
$x-2=0 \rightarrow x=2$
$x^{2}+2x+4=0 \rightarrow x=-1\pm\sqrt 3i$
Thus, the zeros of the function are: $\{2,-1+\sqrt 3i, -1-\sqrt 3i\}$
(b) Completely Factored Form
From part (a) above, the completely factored form of P(x) is:
$P(x)=(x-2)(x^{2}+2x+4)$
