Answer:
f(x) = x³ + x² - 22x - 40
Step-by-step explanation:
Given that x = a is a zero of f(x) then (x - a) is a factor
Here the zeros are x = - 4, x = - 2, x = 5 , then the factors are
(x + 4), (x + 2) and (x - 5)
The function is then the product of the factors, that is
f(x) = (x + 4)(x + 2)(x - 5) ← expand the first pair using FOIL
= (x² + 6x + 8)(x - 5) ← distribute
= x³ + 6x² + 8x - 5x² - 30x - 40 ← collect like terms
= x³ + x² - 22x - 40
