If f (-2) = 0, what are all the factors of the function f (x) = x^3 - 2x^2-68x-120

Use the Remainder Theorem.

A) (x + 2) (x + 60)

B) (x - 2) (x - 60)

C) (x - 10) (x + 2) (x + 6)

D) (x + 10) (x - 2) (x - 6)

F (-2) = 0 ⇒ x+2 is a factor of x^3 - 2x^2 - 68x - 120

Then you can divide x^3 - 2x^2 - 68x - 120 by x + 2.

The quotient of that division is x^2 - 4x - 60 [you should know how to divide polynomilas]

Now factor x^2 - 4x - 60

x^2 - 4x - 60 = (x - 10) (x + 6)

Then the factors are (x+2) (x-10) (x+6)

Which is the option C).