# How do you factor 2x^2 + 7x-4?

Aug 28, 2016

$2 {x}^{2} + 7 x - 4 = \left(2 x - 1\right) \left(x + 4\right)$

#### Explanation:

Use an AC method:

Find a pair of factors of $A C = 2 \cdot 4 = 8$ which differ by $B = 7$

The pair $8 , 1$ works.

Use this pair to split the middle term and factor by grouping:

$2 {x}^{2} + 7 x - 4$

$= 2 {x}^{2} + 8 x - x - 4$

$= \left(2 {x}^{2} + 8 x\right) - \left(x + 4\right)$

$= 2 x \left(x + 4\right) - 1 \left(x + 4\right)$

$= \left(2 x - 1\right) \left(x + 4\right)$