# How do you factor 10x^2 + 5 + 27x?

Jun 6, 2016

$\left(2 x + 5\right) \left(5 x + 1\right)$

#### Explanation:

let's first solve the equation:
$10 {x}^{2} + 27 x + 5 = 0$

and find the zeroes

$x = \frac{- 27 \pm \sqrt{{27}^{2} - 4 \cdot 10 \cdot 5}}{2 \cdot 10}$
then
$x = \frac{- 27 \pm \sqrt{729 - 200}}{20}$
$x = \frac{- 27 \pm 23}{20}$
$x = - \frac{5}{2} \mathmr{and} x = - \frac{1}{5}$

let's factor
$10 {x}^{2} + 27 x + 5 = 10 \left(x + \frac{5}{2}\right) \left(x + \frac{1}{5}\right)$

let's eliminate fractions by multiplying :
$2 \left(x + \frac{5}{2}\right) 5 \left(x + \frac{1}{5}\right)$
$\left(2 x + 5\right) \left(5 x + 1\right)$