Question

How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 1, -1, 2, -2, 3?

Answer 1

`f(x) = x^5-3x^4-5x^3+15x^2+4x-12`

Explanation:

Each zero `a` corresponds to a linear factor `(x-a)`, so we can write:

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

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

`=(x^4-5x^2+4)(x-3)`

`=x^5-3x^4-5x^3+15x^2+4x-12`