Find a polynomial function of degree 3 with - 1, 2, 4 as zeros

f (x) = x³ - 5x² + 2x + 8

Step-by-step explanation:

given the zeros of a polynomial, say x = a and x = b, then

(x - a) and (x - b) are the factors and the polynomial is the product of the factors.

here x = - 1, x = 2 and x = 4 are 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 expanding factors

f (x) = (x + 1) (x² - 6x + 8) = x³ - 5x² + 2x + 8