Fina a polynomial function of degree 3 with real coefficients that has - 1,2,-4 as zeros

f (x) = x³ + 3x² - 6x - 8

Step-by-step explanation:

given the zeros of a polynomial 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 and x = - 4 are the zeros, hence

(x + 1), (x - 2) and (x + 4) are the factors

f (x) = a (x + 1) (x - 2) (x + 4) ← a is a multiplier

let a = 1, then

f (x) = (x + 1) (x - 2) (x + 4)

= (x² - x - 2) (x + 4)

= x³ - x² - 2x + 4x² - 4x - 8

= x³ + 3x² - 6x - 8