Question

How do you write a polynomial in standard form given the zeros x=3,1,2,and-3?

Answer 1

`f(x) = x^4-3x^3-7x^2+27x-18`

Explanation:

The simplest polynomial with these zeros is:

`f(x) = (x-3)(x+3)(x-1)(x-2)`

`= (x^2-9)(x^2-3x+2)`

`= x^4-3x^3-7x^2+27x-18`

Standard form has one term of each degree in descending order of degree (omitting any terms with `0` coefficient).

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