Question

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

Answer 1

`f(x) = x^(3) - x^(2) - 4x +4`

Explanation:

`f(x) = (x - 1) (x +2) (x - 2)` Write a linear factor for each zero.

`= (x - 1) (x + 2)(x - 2)` Multiply
`(x + 2)(x - 2)`

`= (x - 1)(x^(2) - 2x + 2x -4)` Simplify. (The -2x and 2x cancel each other out.)

=
`(x - 1)(x^(2) - 4)` Distribute.

`= (x^(3) -x^(2) -4x + 4)` Simplify.

Answer 2

f(x) = x³ - x² - 4x + 4

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