What is a cubic polynomial function in standard form with zeros 4, -1, and 2

The cubic polynomial would be x^3 - 5x^2 + 2x + 8

Step-by-step explanation:

In order to find this, start with parenthesis for each of the 3 in which we use x and the opposite of the root. This is how we build a polynomial function.

(x - 4)(x + 1)(x - 2)

Now we multiply each together.

(x - 4)(x + 1)(x - 2)

(x^2 - 4x + x - 4)(x - 2)

(x^2 - 3x - 4)(x - 2)

x^3 - 3x^2 - 2x^2  - 4x + 6x + 8

x^3 - 5x^2 + 2x + 8