Question

How do you factor the expression `6x^2 -7x -10`?

Answer 1

`y = (6x + 5)(x - 2)`

Explanation:

I use the systematic, non-guessing, new AC Method to factor trinomials (Socratic Search)
`y = 6x^2 - 7x - 10 =` 6( x + p)(x + q)
Converted trinomial `y' = x^2 - 7x - 60 =` (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = - 60) --> (-2, 30)(-4, 15)(-5, 12). This sum is 7 = -b. Then the opposite sum of (5, -12) gives: p' = 5 and q' = -12.
Therefor, `p = (p')/a = 5/6` and `q = (q')/a = -12/6 = -2.`
Factored form: `y = 6(x + 5/6)(x - 2) = (6x + 5)(x - 2)`