# How do you factor the expression 20x^2 + 13x + 2?

Apr 26, 2016

$20 {x}^{2} + 13 x + 2 = \left(4 x + 1\right) \left(5 x + 2\right)$

#### Explanation:

Use an AC method:

Find a pair of factors of $A C = 20 \cdot 2 = 40$ with sum $B = 13$.

The pair $8 , 5$ works in that $8 \times 5 = 40$ and $8 + 5 = 13$

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

$20 {x}^{2} + 13 x + 2$

$= 20 {x}^{2} + 8 x + 5 x + 2$

$= \left(20 {x}^{2} + 8 x\right) + \left(5 x + 2\right)$

$= 4 x \left(5 x + 2\right) + 1 \left(5 x + 2\right)$

$= \left(4 x + 1\right) \left(5 x + 2\right)$