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:
$P(x)=(x+2)(x^{2}-2x+4)$
