Answer:
see explanation
Step-by-step explanation:
Given the zeros of a polynomial, say x = a, x = b, x = c
Then (x - a), (x - b), (x - c) are it's factors
and the polynomial is the product of the factors
here x = 4, x = - 1, x = 6, hence
(x - 4), (x + 1) and (x - 6) are the factors
f(x) = a(x - 4)(x + 1)(x - 6) ← a is a multiplier
let a = 1, then expanding the first pair of factors
f(x) = (x² - 3x - 4)(x - 6) ← expand out the factors
= x³ - 3x² - 4x - 6x² + 18x + 24 ← collect like terms
= x³ - 9x² + 14x + 24
