# How do you factor completely: 6x^2 + 19x + 10?

Jul 16, 2015

Factor: y = 6x^2 + 19x + 10
y = (3x + 2)(2x + 5)

#### Explanation:

$y = 6 {x}^{2} + 19 x + 10 =$ 6(x - p)(x - q).
I use the new AC Method to factor trinomials (Google, Yahoo search)
Converted $y ' = {x}^{2} + 19 x + 60 =$ (x - p')(x - q'). p' and q' have same sign.
Factor pairs of ac = 60 -> ...(3, 20)(4, 15). This sum is 19 = b.
Then p' = 4 and q' = 15
Then, $p = \frac{4}{6} = \frac{2}{3}$ and $q = \frac{15}{6} = \frac{5}{2}$

$y = 6 \left(x + \frac{2}{3}\right) \left(x + \frac{5}{2}\right) = \left(3 x + 2\right) \left(2 x + 5\right)$