# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3, -3, 1?

Nov 9, 2016

$\textcolor{g r e e n}{f \left(x\right) = {x}^{3} - {x}^{2} - 9 x + 9}$

#### Explanation:

If the polynomial has zeros at $3 , - 3 , \mathmr{and} 1$
then it has factors:
$\textcolor{w h i t e}{\text{XXX}} \left(x - 3\right) , \left(x + 3\right) , \mathmr{and} \left(x - 1\right)$

As a minimal degree polynomial (with leading coefficient $1$)
$\textcolor{w h i t e}{\text{XXX}} \left(x - 3\right) \cdot \left(x + 3\right) \cdot \left(x - 1\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left({x}^{2} - 9\right) \cdot \left(x - 1\right)$

$\textcolor{w h i t e}{\text{XXX}} = {x}^{3} - {x}^{2} - 9 x + 9$