Question

What is a cubic polynomial function in standard form with zeros 1 -2 and 2?

Answer 1

Answer:

f(x) = x³ - x² - 4x + 4

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 the factors of the polynomial and

f(x) is the product of the factors

here x = 1, x = - 2, x = 2, hence

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

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

let a = 1 and expand the factors

f(x) = (x - 1)(x² - 4)

     = x³ - 4x - x² + 4

     = x³ - x² - 4x + 4 ← in standard form