Question

How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 2, 1, 4?

Answer 1

`f(x) = x^3-7x^2+14x-8`

Explanation:

Each zero corresponds to a linear factor, so we can write:

`f(x) = (x-2)(x-1)(x-4) = x^3-7x^2+14x-8`

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