# How do you write a polynomial function with the given zeros 2 and 2i and degree 3?

Mar 31, 2016

You need to write three factors: $\left(x - 2\right) \left(x - 2 i\right) \left(x + 2 i\right)$ based on the Factor Theorem and Complex Conjugates Theorem.
Now, expand the expression: $\left(x - 2\right) \left({x}^{2} + 4\right) = {x}^{3} - 2 {x}^{2} - 4 x - 8$