# How do you factor the expression 15x^2-14x+3 ?

May 12, 2016

$15 {x}^{2} - 14 x + 3 = \left(3 x - 1\right) \left(5 x - 3\right)$

#### Explanation:

Use an AC method:

Find a pair of factors of $A C = 15 \cdot 3 = 45$ with sum $B = 14$.

The pair $9 , 5$ works.

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

$15 {x}^{2} - 14 x + 3$

$= 15 {x}^{2} - 9 x - 5 x + 3$

$= \left(15 {x}^{2} - 9 x\right) - \left(5 x - 3\right)$

$= 3 x \left(5 x - 3\right) - 1 \left(5 x - 3\right)$

$= \left(3 x - 1\right) \left(5 x - 3\right)$