# How do you factor 6x^2 - 25x + 14?

Aug 30, 2016

$6 {x}^{2} - 25 x + 14 = \left(3 x - 2\right) \left(2 x - 7\right)$

#### Explanation:

Given:

$6 {x}^{2} - 25 x + 14$

Use an AC Method:

Look for a pair of factors of $A C = 6 \cdot 14 = 84$ which sum to $B = 25$.

The pair $21 , 4$ works.

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

$6 {x}^{2} - 25 x + 14$

$= 6 {x}^{2} - 21 x - 4 x + 14$

$= \left(6 {x}^{2} - 21 x\right) - \left(4 x - 14\right)$

$= 3 x \left(2 x - 7\right) - 2 \left(2 x - 7\right)$

$= \left(3 x - 2\right) \left(2 x - 7\right)$