# How do you write the simplest polynomial function with the zeros 2i, -2i and 6?

Nov 14, 2016

#### Explanation:

The factor that corresponds to the zero, $2 i$, is $\left(x - 2 i\right)$.
The factor that corresponds to the zero, $- 2 i$, is $\left(x + 2 i\right)$.
The factor that corresponds to the zero, $6$, is $\left(x - 6\right)$.

Collect the factors into an equation:

$y = \left(x - 2 i\right) \left(x + 2 i\right) \left(x - 6\right)$

We can use the pattern, $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$, to multiply the first two factors:

$y = \left({x}^{2} - 4 {i}^{2}\right) \left(x - 6\right)$

Use the property ${i}^{2} = - 1$ to simplify the first factor:

$y = \left({x}^{2} + 4\right) \left(x - 6\right)$

Use the F.O.I.L. method to multiply the remaining factors:

$y = {x}^{3} - 6 {x}^{2} + 4 x - 24$