Answer
Zeros are -3, 2, 5
Factored Form: $(x+3)^2(x-2)(x-5)$
Work Step by Step
The question asks for the zeros and the polynomial in factored form
Given $P(x) = x^4 - x^3 - 23x^2 - 3x + 90$
Synthetic division will be used for the first two factors, then factoring will be used for the last two.
In the image below, 5 and 2 are factors for P(x), so two factors are (x-5) and (x-2)
Thus $P(x) = (x^2 + 6x + 9) (x-5)(x-2)$
Factor $x^2 + 6x + 9$
=$(x+3)^2$
Thus the zeros are x = -3, 2, 5
The factored form is $(x+3)^2(x-2)(x-5)$
