Answer:
f(x) = x³ - x² - 4x + 4
Step-by-step explanation:
Given the zeros of a polynomial say x = a, x = b, x = c then
(x - a), (x - b), (x - c) are the factors of the polynomial and
f(x) is the product of the factors
here x = 1, x = - 2, x = 2, hence
(x - 1),(x + 2), (x - 2) are the factors and
f(x) = a(x - 1)(x + 2)(x - 2) ← a is a multiplier
let a = 1 and expand the factors
f(x) = (x - 1)(x² - 4)
= x³ - 4x - x² + 4
= x³ - x² - 4x + 4 ← in standard form
