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

Mar 3, 2018

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:

$\left(x - 9\right) \left(x - 9\right) \left(x - 9\right) = 0$

We can expand the left hand side to get

x^3−27x^2+243x−729