# How do you factor x^2 - 12x + 34?

Aug 30, 2016

${x}^{2} - 12 x + 34 = \left(x - 6 - \sqrt{2}\right) \left(x - 6 + \sqrt{2}\right)$

#### Explanation:

Complete the square then use the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = \left(x - 6\right)$ and $b = \sqrt{2}$ as follows:

${x}^{2} - 12 x + 34$

$= {x}^{2} - 12 x + 36 - 2$

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

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

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