# How do you factor completely  4x^2 - 28x +40?

Apr 8, 2016

$4 {x}^{2} - 28 x + 40 = 4 \left(x - 5\right) \left(x - 2\right)$

#### Explanation:

$4 {x}^{2} - 28 x + 40 = 4 \textcolor{red}{\left({x}^{2} - 7 x + 10\right)}$

$\textcolor{red}{{x}^{2} - 7 x + 10} = \left(x - 5\right) \left(x - 2\right)$

$4 {x}^{2} - 28 x + 40 = 4 \left(x - 5\right) \left(x - 2\right)$

Apr 8, 2016

$4 {x}^{2} - 28 x + 40 = \textcolor{g r e e n}{4 \left(x - 5\right) \left(x - 2\right)}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 4 {x}^{2} - 28 x + 40$
Extract the simple constant factor of $4$
$\textcolor{w h i t e}{\text{XXX}} = 4 \left({x}^{2} - 7 x + 10\right)$factor the second part by inspection or use of the quadratic formula to get
$\textcolor{w h i t e}{\text{XXX}} = 4 \left(x - 2\right) \left(x - 5\right)$