Question

How do you write a polynomial function given the real zeroes -2, -1, 0, 1, and 2 and coefficient 1?

Answer 1

`f(x) = x^5-5x^3+4x`

Explanation:

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

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

`=(x^4-5x^2+4)x`

`=x^5-5x^3+4x`

This is the simplest polynomial in `x` with the required zeros.

Any other polynomial in `x` with these zeros is a multiple (scalar or polynomial) of this `f(x)`.

The polynomial graphed:

graph{x^5-5x^3+4x [-10, 10, -5, 5]}