# What is a polynomial function for 5, i, -i?

Sep 19, 2016

$f \left(x\right) = {x}^{3} - 5 {x}^{2} + x - 5$

#### Explanation:

I have assumed that $\left\{5 , i , - i\right\}$ are intended to be the zeros of the function.

In this case, the function can be factored as:
color(white)("XXX")(x-5)((x-i)(x+i)

$\textcolor{w h i t e}{\text{XXX}} = \left(x - 5\right) \left({x}^{2} - {i}^{2}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left(x - 5\right) \left({x}^{2} + 1\right)$

$\textcolor{w h i t e}{\text{XXX}} = {x}^{3} + x - 5 {x}^{x} - 5$

(or in standard polynomial form)
$\textcolor{w h i t e}{\text{XXX}} = {x}^{3} - 5 {x}^{2} + x - 5$