Question

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

Answer 1

`f(x) = x^4-4x^3-x^2+16x-12`

Explanation:

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

`= (x-3)(x-1)(x^2-4)`

`= (x-3)(x^3-x^2-4x+4)`

`= x^4-4x^3-x^2+16x-12`

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