Question

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

Answer 1

The simplest such polynomial would be `color(blue)(x^3-6x^2+11x-6)`

Explanation:

If `1, 2, and 3` are zeros of the polynomial then the polynomial must contain (at least) factors:
`color(white)("XXX")(x-1)`
`color(white)("XXX")(x-2)` and
`color(white)("XXX")(x-3)`

If these are the only factors then our polynomial is
`color(white)("XXX")(x-1)(x-2)(x-3)`

To express this in standard form we need to expand by multiplying and make sure that the terms are listed in descending degree.