# How do you factor completely: 2x^2 - 6x - 56?

Jul 18, 2015

Separate out the scalar factor $2$ then find pair of numbers $4$ and $7$ whose product is $28$ and difference $3$, hence...

$2 {x}^{2} - 6 x - 56 = 2 \left(x - 7\right) \left(x + 4\right)$

#### Explanation:

$2 {x}^{2} - 6 x - 56 = 2 \left({x}^{2} - 3 x - 28\right)$

To factor ${x}^{2} - 3 x - 28$, find a pair of numbers whose product is $28$ and whose difference is $3$. The pair $7$, $4$ works.

So ${x}^{2} - 3 x - 28 = \left(x - 7\right) \left(x + 4\right)$

and

$2 {x}^{2} - 6 x - 56 = 2 \left(x - 7\right) \left(x + 4\right)$