# How do you find the polynomial function that has the given zeros: 0, -4, and -3?

The simplest answer is $x \left(x + 4\right) \left(x + 3\right) = x \left({x}^{2} + 7 x + 12\right) = {x}^{3} + 7 {x}^{2} + 12 x$. Any nonzero scalar multiple of this also works.
In general, if you want $x = c$ to be a root of a polynomial, then the polynomial must contain at least one factor of the form $x - c$ (if $c < 0$ the $x - c$ can be written as an addition of a positive number).