Find a cubic function with the given zeros -6, 7, -4

y    = x^3 - 7x^2 - 36x - 168

Step-by-step explanation:

Hello!

If your zeros ae -6, -4 and 7, then your factors are (x+6), (x+4) and (x-7).  To find the desired cubic function, multiply these three factors together:

y = f(x) = (x^2 + 4x + 6x + 24)(x - 7).

          =  (x^2 +     10x + 24)(x - 7)

          = x^3 - 7x^2 + 10x - 70x + 24x - 168

      y    = x^3 - 7x^2 - 36x - 168 (answer)

Note how these terms are arranged in descending powers of x.

(x-(-6)) (x-7) (x-(-4))

(x+6) (x-7) (x+4)

x^3 + 3 x^2 - 46 x - 168