# How do you factor completely 5x^2 - 23 x + 12?

Mar 17, 2016

Use an AC method and factor by grouping to find:

$5 {x}^{2} - 23 x + 12 = \left(5 x - 3\right) \left(x - 4\right)$

#### Explanation:

We can use an AC method.

Look for a pair of factors of $A C = 5 \cdot 12 = 60$ with sum $B = 23$.

The pair $20 , 3$ works.

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

$5 {x}^{2} - 23 x + 12$

$= 5 {x}^{2} - 20 x - 3 x + 12$

$= \left(5 {x}^{2} - 20 x\right) - \left(3 x - 12\right)$

$= 5 x \left(x - 4\right) - 3 \left(x - 4\right)$

$= \left(5 x - 3\right) \left(x - 4\right)$