Question

How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -6, 3, 5?

Answer 1

`f(x) = (x+6)(x-3)(x-5) = x^3-2x^2-33x+90`

Explanation:

For each zero `a`, the polynomial must have a corresponding linear factor `(x-a)`.

So the polynomial of least degree with all three zeros is:

`f(x) = (x+6)(x-3)(x-5) = x^3-2x^2-33x+90`

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