Question

How do you factor `6x^2+5x-4`?

Answer 1

(2x - 1)( 3x + 4)

Explanation:

Use the new AC Method (Socratic Search)
`y = 6x^2 + 5x - 4 =` 6(x + p)(x + q)
Converted trinomial: `y' = x^2 + 5x - 24 =` (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
factor pairs of (ac = - 24) --> (-3, 8). This sum is (5 = b). Then p' = -3 and q' = 8.
Back to trinomial y --> `p = (p')/a = -3/6 = -1/2`, and `q = (q')/a = 8/6 = 4/3`.
Factored form `y = 6(x - 1/2)(x + 4/3) = (2x - 1)(3x + 4)`