Question

How do you find a polynomial function that has zeros `x=9` and degree n=3?

Answer 1

The polynomial is `x^3−27x^2+243x−729`

Explanation:

The question implies that all of the zeros of the cubic (degree 3) polynomial are at the same point, `x=9`. We can easily form the polynomial by writing it in factored form at the zero:

`(x-9)(x-9)(x-9)=0`

We can expand the left hand side to get

`x^3−27x^2+243x−729`