Question

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

Answer 1

(2x + 3)(x + 4)

Explanation:

Use the new AC Method (Socratic Search)
`y = 2x^2 + 11x + 12 =` 2(x + p)(x + q)
Converted trinomial `y' = x^2 + 11x + 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 = (p')/a = 3/2`, and `q = (q')/a = 8/2 = 4.`
Factored form:`y = 2(x + 3/2)(x + 4) = (2x + 3)(x + 4)`