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

Nov 12, 2015

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

#### Explanation:

I (personally) always find it easier to work with expressions in standard form, so I will re-write the given expression as
$\textcolor{w h i t e}{\text{XXX}} - 2 {x}^{2} + 6 x + 20$

As a first step extract the obvious constant factor:
$\textcolor{w h i t e}{\text{XXX}} \left(- 2\right) \left({x}^{2} - 3 x - 10\right)$

To factor the second part, we are looking for factors of $10$ whose difference is $3$.
Again with only a bit of consideration we can come up with $\left(2 , 5\right)$

Since the constant term $\left(- 10\right)$ is negative, we know that one of $\left(2 , 5\right)$ is negative.
Since the coefficient of $x$ (i.e. $\left(- 3\right)$) is also negative we know that the larger of $\left(2 , 5\right)$ should be negative.

Therefore we can factor our expression as
$\textcolor{w h i t e}{\text{XXX}} \left(- 2\right) \left(x - 5\right) \left(x + 2\right)$