# How do you write P(x) = x^3 − 27x − 54 in factored form?

Apr 18, 2018

${x}^{3} - 27 x - 54 = \left(x - 6\right) {\left(x + 3\right)}^{2}$

#### Explanation:

${x}^{3} - 27 x - 54$

First note that $P \left(- 3\right) = 0$. This means that $x + 3$ is a factor of $P \left(x\right)$. Lets synthetically divide $P \left(x\right)$ by $x + 3$ and see what remains.

${x}^{3} - 27 x - 54 = {x}^{3} + 3 {x}^{2} - 3 {x}^{2} - 9 x - 18 x - 54$

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

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

$= \left(x - 6\right) \left(x + 3\right) \left(x + 3\right)$

$= \left(x - 6\right) {\left(x + 3\right)}^{2}$