# Is it possible to factor y=x^2 + 7x – 6 ? If so, what are the factors?

Apr 7, 2018

$\left(x + \frac{7}{2} - \frac{1}{2} \sqrt{73}\right) \left(x + \frac{7}{2} + \frac{1}{2} \sqrt{73}\right)$

#### Explanation:

$\text{there are no whole number factors of - 6 which sum}$
$\text{+ 7}$

$\text{obtain the factors by finding the solution using the }$
$\textcolor{b l u e}{\text{quadratic formula}}$

•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)

$\text{with "a=1,b=7" and } c = - 6$

$x = \frac{- 7 \pm \sqrt{49 + 24}}{2} = \frac{- 7 \pm \sqrt{73}}{2}$

$x = - \frac{7}{2} + \frac{1}{2} \sqrt{73} \text{ or } x = - \frac{7}{2} - \frac{1}{2} \sqrt{73}$

$\text{thus the factors are}$

$\left(x - \left(- \frac{7}{2} + \frac{1}{2} \sqrt{73}\right)\right) \left(x - \left(- \frac{7}{2} - \frac{1}{2} \sqrt{73}\right)\right)$

$= \left(x + \frac{7}{2} - \frac{1}{2} \sqrt{73}\right) \left(x + \frac{7}{2} + \frac{1}{2} \sqrt{73}\right)$