# How do you write a polynomial function of least degree that has real coefficients, the following given zeros -2,-2,3,-4i and a leading coefficient of 1?

${\left(x + 2\right)}^{2} \left(x - \left(3 - 4 i\right)\right) \left(x + \left(3 - 4 i\right)\right)$
-2 has a multiplicity of 2 so you can start out with ${\left(x + 2\right)}^{2}$ and since $3 - 4 i$ is a zero you can multiply it, so: ${\left(x + 2\right)}^{2} \left(x - \left(3 - 4 i\right)\right)$ and if you need real coefficients the other zero would have to be $3 + 4 i$ because this is the only way to eliminate the $i$ in this function so, ${\left(x + 2\right)}^{2} \left(x - \left(3 - 4 i\right)\right) \left(x + \left(3 - 4 i\right)\right)$