The wording of the problem seems off to me! "Find the cubic equation that has zeros at -8, -4, and 13 if f(-10)=-138" Where in the world did "f" come from? The problem is to find an **equation**, not a function! There is no "f"! The wording **should** be "Find the equation, of the form f(x)= 0, that has zeros at -8, -4, and 13 if f(-10)=-138".

It certainly is true that a cubic equation that has zeroes at x= -8, x= -4, and x= 13 must be of the form

a(x+ 8)(x+ 4)(x- 13)= 0.

I see nothing In this problem that asks us to multiply that out! Instead, since this is "f(x)= 0" and we must have f(-10)= -138, write f(-10)= a(-10+ 8)(-10+ 4)(-10- 13)= a(-2)(-6)(-23)= -276a= -138 so a= 138/276= 1/2.

The problem asked for an **equation** not a function so my answer would be

(1/2)(x+ 8)(x+ 4)(x- 13)= 0.