# How do you write a polynomial function given the real zeroes 2,-2,-6i and coefficient 1?

$\left(x - 2\right) \left(x + 2\right) \left(x + 6 i\right) = \left({x}^{2} - 4\right) \left(x + 6 i\right) = {x}^{3} + 6 i {x}^{2} - 4 x - 24 i$
Generally if a polynomial function with grade n has zeroes ${x}_{1} , {x}_{2} , \ldots , {x}_{n}$ then $P \left(x\right) = a \left(x - {x}_{1}\right) \left(x - {x}_{2}\right) \ldots \left(x - {x}_{n}\right)$
where a is the coefficient of ${x}^{n}$