Answer
$(x-2) (x + 1 - i) (x +1 + i)$
Zeros: $2, -1 + i, -1 - i$
Work Step by Step
The question asks for the real zeros and complete factorization of P(x)
Given $P(x) = x^3 - 2x - 4$
See the synthetic division below.
After the division, the factorization is $(x-2)(x^2 + 2x + 2)$
Set each polynomial equal to zero
$x - 2 = 0$
$x = 2$
$x^2 + 2x + 2 = 0$
$x^2 + 2x + 1 = -1$
$(x+1)^2 = -1$
$x = -1 +/- i $
Thus the complete factorization is $(x-2) (x + 1 - i) (x +1 + i)$
The zeros are $2, -1 + i, -1 - i$
