# How do you factor y= 6x^2 + 20x + 6 ?

Feb 28, 2016

y = 2(3x + 1)(x + 3)

#### Explanation:

Use the new AC Method to factor trinomial. (Socratic Search)
$y = 6 {x}^{2} + 20 x + 6$.
Converted trinomial: ${x}^{2} + 20 x + 36 =$ (x + p')(x + q').
Factor pairs of 36 --> (2, 18) This sum is 20 = b. Then p' = 2 and q' = 18
Back to original trinomial: $p = \frac{2}{6} = \frac{1}{3}$ and $q = \frac{18}{6} = 3.$
Factored form: $y = 6 \left(x + \frac{1}{3}\right) \left(x + 3\right) = 2 \left(3 x + 1\right) \left(x + 3\right)$