# How do you factor 2x^2 + 11x + 12 ?

May 26, 2016

(2x + 3)(x + 4)

#### Explanation:

Use the new AC Method (Socratic Search)
$y = 2 {x}^{2} + 11 x + 12 =$ 2(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) -->... (3, 8). This sum is 11 = b. Then p' = 3 and q' = 8.
Back to original y,$p = \frac{p '}{a} = \frac{3}{2}$, and $q = \frac{q '}{a} = \frac{8}{2} = 4.$
Factored form:$y = 2 \left(x + \frac{3}{2}\right) \left(x + 4\right) = \left(2 x + 3\right) \left(x + 4\right)$