Question

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

Answer 1

`f(x) = x^3-x^2-6x`

Explanation:

Each zero corresponds to a linear factor, so we can define:

`f(x) = (x-3)(x-0)(x+2)=x(x-3)(x+2)=x^3-x^2-6x`

Any polynomial in `x` with these zeros will be a multiple (scalar or polynomial) of this `f(x)`.