Answer:
f(x) = x³ - 2x² - 16x + 32
Step-by-step explanation:
Given the zeros of a polynomial say x = a, x = b, x= c
Then the factors of the polynomial are (x - a), (x - b), (x - c)
and the polynomial is the product of the factors
f(x) = a(x - a)(x - b)(x - c) ← a is a multiplier
Here x = - 4, x = 4, x = 2, thus the factors are
(x + 4), (x - 4) and (x - 2), thus let a = 1 gives
f(x) = (x + 4)(x - 4)(x - 2) ← expand the first pair of factors using FOIL
= (x² - 16)(x - 2) ← distribute
= x³ - 2x² - 16x + 32 ← polynomial of degree 3
