# How do you write a polynomial function that has the zeros 3, -3, and 2 and has a leading coefficient of 1?

Mar 29, 2016

There is a theorem that says "if c is a zero, then x - c is a factor".

#### Explanation:

The polynomial would be f(x) = (x - 3)(x + 3) (x - 2). If you wish to write it in an expanded form, start to distribute terms.

$f \left(x\right) = \left({x}^{2} - 9\right) \left(x - 2\right)$
$f \left(x\right) = {x}^{3} - 2 {x}^{2} - 9 x + 18$