# Is it possible to factor y=2x^2 -452x-68? If so, what are the factors?

Jun 29, 2016

$y = 2 \left(x - 113 + \sqrt{12803}\right) \left(x - 113 - \sqrt{12803}\right)$

#### Explanation:

Step 1: Removing the obvious integer common factor:
$\textcolor{w h i t e}{\text{XXX}} y = 2 \left({x}^{2} - 226 - 35\right)$

From this point on there are no "pretty" factors but...
Step 2: Use the quadratic formula to find the roots

For the general quadratic: $a {x}^{2} + b x + c$ the roots are given by:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this case
$\textcolor{w h i t e}{\text{XXX}} x = \frac{226 \pm \sqrt{{\left(- 226\right)}^{2} - 4 \left(1\right) \left(- 35\right)}}{2 \left(1\right)}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \frac{226 \pm \sqrt{51212}}{2} = 113 \pm \sqrt{12803}$

So we can continue the factoring as:
$\textcolor{w h i t e}{\text{XXX}} y = 2 \left(x - 113 + \sqrt{12803}\right) \left(x - 113 - \sqrt{12803}\right)$