Answer:
f(x) = x³ - 4x² - 25x + 28
Explanation:
Given the zeros x = 1, x = 7 and x = - 4 , then the corresponding factors are
(x - 1), (x - 7), (x + 4)
The polynomial is then the product of the factors, that is
f(x) = a(x - 1)(x - 7)(x + 4) , a is a multiplier
let a = 1 and expand the first pair of factors using FOIL
f(x) = (x² - 8x + 7)(x + 4) ← distribute
= x³ - 8x² + 7x + 4x² - 32x + 28 ← collect like terms
= x³ - 4x² - 25x + 28