# How do you write the polynomial function given the following zeros: -3, -2i, 2i?

$f \left(x\right) = {x}^{3} + 3 {x}^{2} + 4 x + 12$
$f \left(x\right) = \left(x + 3\right) \left(x + 2 i\right) \left(x - 2 i\right) = \left(x + 3\right) \left({x}^{2} + 4\right)$
$= {x}^{3} + 3 {x}^{2} + 4 x + 12$
Any polynomial in $x$ with these roots will be a multiple (scalar of polynomial) of this $f \left(x\right)$.