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

Answer 1

To find a cubic polynomial function in standard form with zeros 1, -2, and 2, we use the fact that if a number is a zero of a polynomial, then the polynomial can be factored by (x - z), where z represents the zero.

So, the polynomial can be factored as (x - 1)(x - (-2))(x - 2).

Expanding this expression gives:

(x - 1)(x + 2)(x - 2) = (x^2 - x + 2x - 2)(x - 2)
= (x^2 + x - 2)(x - 2)
= x^3 + x^2 - 2x - 2x^2 - 2x + 4
= x^3 - x^2 - 4x + 4

Therefore, a cubic polynomial function in standard form with zeros 1, -2, and 2 is:

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