# How do you write a polynomial with roots 3, –3, and 3 ?

${x}^{3} - 3 {x}^{2} - 9 x + 27 = 0$

#### Explanation:

From the given: The roots are

$x = 3$ and $x = - 3$ and $x = 3$

$x - 3 = 0$ and $x + 3 = 0$ and $x - 3 = 0$

Multiply them all and equate to zero

$\left(x - 3\right) \left(x + 3\right) \left(x - 3\right) = 0$

$\left(x - 3\right) \left({x}^{2} - 9\right) = 0$

$\left({x}^{3} - 9 x - 3 {x}^{2} + 27\right) = 0$

rearanging

${x}^{3} - 3 {x}^{2} - 9 x + 27 = 0$

God bless....I hope the explanation is useful.