# How do you factor 3x^2 - 19x +6 = 0 ?

Oct 28, 2016

$0 = 3 {x}^{2} - 19 x + 6 = \left(3 x - 1\right) \left(x - 6\right)$

#### Explanation:

$3 {x}^{2} - 19 x + 6 = 0$

Use an AC Method:

Find a pair of factors of $A C = 3 \cdot 6 = 18$ with sum $B = 19$

The pair $18 , 1$ works in that $18 + 1 = 19$ and $18 \cdot 1 = 18$.

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

$3 {x}^{2} - 19 x + 6 = 3 {x}^{2} - 18 x - x + 6$

$\textcolor{w h i t e}{3 {x}^{2} - 19 x + 6} = \left(3 {x}^{2} - 18 x\right) - \left(x - 6\right)$

$\textcolor{w h i t e}{3 {x}^{2} - 19 x + 6} = 3 x \left(x - 6\right) - 1 \left(x - 6\right)$

$\textcolor{w h i t e}{3 {x}^{2} - 19 x + 6} = \left(3 x - 1\right) \left(x - 6\right)$