Answer:
f(x) = x³ - 2x² - 19x + 20
Step-by-step explanation:
Given a polynomial with zeros x = a, x = b then the corresponding factors are
(x - a)(x - b) and the polynomial is then the product of the factors
Given zeros x = 5, x = - 4, x = 1 , then
(x - 5), (x + 4) and (x - 1) are the factors, then
f(x) = (x - 5)(x + 4)(x - 1) ← expand the first pair of factors using FOIL
= (x² - x - 20)(x - 1) ← distribute
= x³ - x² - 20x - x² + x + 20 ← collect like terms
= x³ - 2x² - 19x + 20
