Answer:
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
