# How do you factor 5x^2 - 26x +5 ?

Feb 20, 2017

#### Answer:

$5 {x}^{2} - 26 x + 5 = \left(5 x - 1\right) \left(x - 5\right)$

#### Explanation:

Given:

$5 {x}^{2} - 26 x + 5$

Use an AC method:

Find a pair of factors of $A C = 25$ with sum $B = 26$

The pair $25 , 1$ works.

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

$5 {x}^{2} - 26 x + 5 = 5 {x}^{2} - 25 x - x + 5$

$\textcolor{w h i t e}{5 {x}^{2} - 26 x + 5} = \left(5 {x}^{2} - 25 x\right) - \left(x - 5\right)$

$\textcolor{w h i t e}{5 {x}^{2} - 26 x + 5} = 5 x \left(x - 5\right) - 1 \left(x - 5\right)$

$\textcolor{w h i t e}{5 {x}^{2} - 26 x + 5} = \left(5 x - 1\right) \left(x - 5\right)$