Question

How do you factor `6x^2 + 13x -5`?

Answer 1

y = (3x - 1)(2x + 5)

Explanation:

I use the systematic (non- guessing) AC Method to factor trinomials (Socratic Search).
`y = 6x^2 + 13x - 5 =` 6(x + p)(x + q)
Converted trinomial: `y' = x^2 + 13x - 30 =` (x + p')(x + q').
p' and q' have opposite signs, because ac < 0.
Factor pairs of (ac = -30) --> (-2, 15). This sum is (13 = b). Then p' = -2 and q' = 15.
Back to original trinomial, p = (p')/a = -2/6 = -1/3 and q = (q')/a = 15/6 = 5/2
Factored form: y = 6(x - 1/3)(x + 5/2) = (3x - 1)(2x + 5)