# How do you factor the expression 3x^2-3x-18?

Jan 15, 2016

Take three common and then find the roots of the quadratic equation.

#### Explanation:

$3 {x}^{2} - 3 x - 18 = 3 \left({x}^{2} - x - 9\right)$
for the quadratic equation ${x}^{2} - x - 9 = 0$ a=1, b=-1, c=-9
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$x = \frac{1 \pm \sqrt{37}}{2}$
therefore
$3 {x}^{2} - 3 x - 18 = 3 \left(x - \frac{1 + \sqrt{37}}{2}\right) \left(x - \frac{1 - \sqrt{37}}{2}\right)$