How do you determine the x values that cause this polynomial to be a function of zero, positive, or negative? F(x)=(x+2)(x+1)(x-5)

It's negative if 1 of the factors is negative. It's positive if all or 1 of the factors is positive. Both of these are assuming that it's none of the factors are equal to 0. It's equal to 0 if any of the factors are equal to 0.