# How do you factor y= 6x^2 + 11x + 4 ?

May 30, 2016

$y = \left(2 x + 1\right) \left(3 x + 4\right)$

#### Explanation:

$y = 6 {x}^{2} + 11 x + 4$

$y = \left(2 x + 1\right) \left(3 x + 4\right)$

May 30, 2016

y = (2x + 1)(3x + 4)

#### Explanation:

Use the new AC Method (Socratic Search)
$y = 6 {x}^{2} + 11 x + 4 =$ 6(x + p)(x + q)
Converted trinomial: $y ' = {x}^{2} + 11 x + 24 =$ (x + p')(x + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 24) --> ...(2, 12)(3, 8). This sum is 11 = b. Then, p' 3 and q' = 8.
Back to the original y --> $p = \frac{p '}{a} = \frac{3}{6} = \frac{1}{2}$, and
$q = \frac{q '}{a} = \frac{8}{6} = \frac{4}{3}$
Factored form: $y = 6 \left(x + \frac{1}{2}\right) \left(x + \frac{4}{3}\right) = \left(2 x + 1\right) \left(3 x + 4\right)$