Question

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

Answer 1

The simplest answer is `x(x+4)(x+3)=x(x^2+7x+12)=x^3+7x^2+12x`. Any nonzero scalar multiple of this also works.

Explanation:

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).