# How do you factor 6 + 7x - 20x^2?

Oct 9, 2017

$6 - 7 x - 20 {x}^{2} = \left(3 - 4 x\right) \left(2 + 5 x\right)$

#### Explanation:

Find factors of $6 \mathmr{and} 20$ which differ by $7$

$\text{ "6" } 20$
$\text{ "darr" } \downarrow$

$\text{ "3" "4" } \rightarrow 2 \times 4 = 8$
$\text{ "2" "5" } \rightarrow 3 \times 5 = \underline{15}$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times x} 7$

We have the correct factors, now add in the signs.

We need $- 20$ and $+ 7$

$\text{ "3" "-4" } \rightarrow 2 \times - 4 = - 8$
$\text{ "2" "+5" } \rightarrow 3 \times + 5 = + \underline{15}$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times x} + 7$

$6 - 7 x - 20 {x}^{2} = \left(3 - 4 x\right) \left(2 + 5 x\right)$