Answer
Zeros are -4, -2, -1, 1
Factored form: $(x+4)(x+2)(x+1)(x-1)$
Work Step by Step
The question asks for the zeros and the polynomial in factored form
Given $P(x) = x^4 + 6x^3 + 7x^2 - 6x - 8$
Synthetic division will be used for the first two factors, then factoring will be used for the last two.
In the image below, 1 and -1 are factors for P(x), so two factors are (x-1) and (x+1)
Thus $P(x) = (x^2 + 6x + 8) (x+1) (x-1)$
Factor $x^2 + 6x + 8$
=$(x+2)(x+4)$
Thus the zeros are x = -4, -2, -1, 1
The factored form is $(x+4)(x+2)(x+1)(x-1)$
