Answer
True; see explanation below
Work Step by Step
The problem asks to prove that a factor is a zero of the polynomial
Given $P(x) = x^5 + 4x^4 - 7x^3 - 23x^2 + 23x + 12$ and x+4
Thus the factor is x= -4
Substitute x = -4 into P(x)
$P(-4) = (-4)^5 + 4(-4)^4 - 7 (-4)^3 - 23(-4)^2 + 23 (-4) + 12$
$P(-4) = -1024 + 1024 + 448 - 368 - 92 + 12= 0$
Thus x+4 is a zero of the polynomial