Question

How do you write a polynomial function in standard form with the given zeros: -1, 3, 5?

Answer 1

The simplest such (non-zero) polynomial is:

`f(x) =x^3-7x^2+7x+15`

Explanation:

As a product of linear factors, we can define:

`f(x) = (x+1)(x-3)(x-5)`

`=(x+1)(x^2-8x+15)`

`=x^3-7x^2+7x+15`

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