Question

How do you write a polynomial in standard form given the zeros x= -1, 3, 5?

Answer 1

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

Explanation:

Each zero corresponds to a linear factor...

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

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

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

This is in standard form, with the terms arranged in descending degree.

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