Question

How do you factor `12x²-26x-10`?

Answer 1

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

Explanation:

`y = 2y' = 2(6x^2 - 13x - 5)`
Factor y', the trinomial in parenthese by the new AC Method (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 trinomial y' --> `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)`