# How do you factor 5z + 8yx + 4yz + 10x ?

Apr 6, 2016

$\left(5 + 4 y\right) \left(z + 2 x\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 5 z + 8 y x + 4 y z + 10 x$

Recognizing the $1 : 2$ ratio of $5 : 10$ and $4 : 8$
we can regroup the terms as
$\textcolor{w h i t e}{\text{XXX}} \left(5 z + 10 x\right) + \left(4 y z + 8 y x\right)$
then extract common factors from each pair of terms:
$\textcolor{w h i t e}{\text{XXX}} 5 \left(z + 2 x\right) + 4 y \left(z + 2 x\right)$

Recognize the common factor: $\left(z + 2 x\right)$
$\textcolor{w h i t e}{\text{XXX}} \left(5 + 4 y\right) \left(z + 2 x\right)$