# How do you factor 5n^2-22n+8?

Jul 1, 2016

$5 {n}^{2} - 22 n + 8 = \left(5 n - 2\right) \left(n - 4\right)$

#### Explanation:

Use an AC method:

Find a pair of factors of $A C = 5 \cdot 8 = 40$ with sum $B = 22$

The pair $20 , 2$ works.

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

$5 {n}^{2} - 22 n + 8 = \left(5 {n}^{2} - 20 n\right) - \left(2 n - 8\right)$

$= 5 n \left(n - 4\right) - 2 \left(n - 4\right)$

$= \left(5 n - 2\right) \left(n - 4\right)$