What is a cubic polynomial function in standard form with zeros 1, -2, and 2?
x³ + x² - 3x + 4
x³ + x² - 4x - 2
x³ + x² + 4x + 4
x³ - x² - 4x + 4

Solution:

Given, the zeros of the cubic polynomial function are 1, -2 and 2.

We have to find the equation of the cubic polynomial in standard form.

Zeros implies the factors of the polynomial.

x - 1 = 0

x + 2 = 0

x - 2 = 0

So, (x - 1) (x - 2) (x + 2) = 0

By using the multiplicative distributive property

(x² - 2x - x + 2) ( x + 2) = 0

(x² - 3x + 2) (x + 2) = 0

So we get

x³ + 2x² - 3x² - 6x + 2x + 4 = 0

x³ - x² - 4x + 4 = 0

Therefore, the cubic polynomial function is x³ - x² - 4x + 4 = 0.

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

Summary:

x³ - x² - 4x + 4 = 0 is a cubic polynomial function in standard form with zeros 1, -2, and 2.