# How do you write a polynomial function of least degree with integral coefficients that has the given zeroes 4, -1, -3i?

$p \left(z\right) = {z}^{4} - 3 {z}^{3} + 5 {z}^{2} - 27 z - 36$
$p \left(z\right) = \left(z - 4\right) \left(z + 1\right) \left(z - 3 i\right) \left(z + 3 i\right)$
$= \left({z}^{2} - 3 z - 4\right) \left({z}^{2} + 9\right)$
$= {z}^{4} - 3 {z}^{3} - 4 {z}^{2} + 9 {z}^{2} - 27 z - 36$