# How do you factor completely x^2 - 3x - 24?

Nov 19, 2015

Use the quadratic formula to find:

${x}^{2} - 3 x - 24 = \left(x - \frac{3 + \sqrt{105}}{2}\right) \left(x - \frac{3 - \sqrt{105}}{2}\right)$

#### Explanation:

${x}^{2} - 3 x - 24$ is in the form $a {x}^{2} + b x + c$ with $a = 1$, $b = - 3$ and $c = - 3$ and has zeros given by the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$= \frac{3 \pm \sqrt{{\left(- 3\right)}^{2} - \left(4 \times 1 \times \left(- 24\right)\right)}}{2 \times 1}$

$= \frac{3 \pm \sqrt{9 + 96}}{2}$

$= \frac{3 \pm \sqrt{105}}{2}$

Hence:

${x}^{2} - 3 x - 24 = \left(x - \frac{3 + \sqrt{105}}{2}\right) \left(x - \frac{3 - \sqrt{105}}{2}\right)$