The degree of the polynomial function f (x) is 3. The roots of the equation f (x) = 0 are - 4,0, and 2

We can take these factors and multiply them in order to find the function you're referring to.

(x) (x + 4) (x - 2)

(x) (x^2 - 2x + 4x - 8)

(x) (x^2 + 2x - 8)

(x^3 + 2x^2 - 8x) is the polynomial referred to in the question.