Question

How do you write a polynomial in standard form given zeros 4i,4, and -4i?

Answer 1

Start from factored form to find that one such polynomial is

`x^3-4x^2+16x-64`

Explanation:

To create a polynomial with a given set of zeros, we can use the fact that `a` is a zero of a polynomial if and only if `(x-a)` is a factor of the polynomial. Then, starting from the zeros, we can simply take the product of all such factors.

`(x-4)(x-4i)(x-(-4i)) = (x-4)(x-4i)(x+4i)`

`=(x-4)(x^2+16)`

`=x^3-4x^2+16x-64`