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).

What exactly is your question?