# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3, 0, -2?

$f \left(x\right) = {x}^{3} - {x}^{2} - 6 x$
$f \left(x\right) = \left(x - 3\right) \left(x - 0\right) \left(x + 2\right) = x \left(x - 3\right) \left(x + 2\right) = {x}^{3} - {x}^{2} - 6 x$
Any polynomial in $x$ with these zeros will be a multiple (scalar or polynomial) of this $f \left(x\right)$.