# How do you factor x^3-3x^2-81x+243?

Jun 21, 2016

$= \left(x - 3\right) \left(x + 9\right) \left(x - 9\right)$

#### Explanation:

If an expression has 4 more more terms, group them in pairs (or threes) first - making sure there is + sign between the groups.

$\left({x}^{3} - 3 {x}^{2}\right) + \left(- 81 x + 243\right) \text{ look for a common factor}$

$= {x}^{2} \left(x - 3\right) - 81 \left(x - 3\right)$

Note that -81 was used as a common factor so the sign in the second bracket changed.
$= \left(x - 3\right) \left({x}^{2} - 81\right) \text{ difference of squares}$

$= \left(x - 3\right) \left(x + 9\right) \left(x - 9\right)$