Question

How do you factor the expression `12m^2 - 7m -10`?

Answer 1

y = (3x + 2)(4x - 5)

Explanation:

Use the new systematic AC Method to factor trinomials (Socratic Search)
`y = 12m^2 - 7m - 10 =` 12(x + p)(x + q)
Converted trinomial: `y' = m^2 - 7m - 120 =` (x + p')(x + q')
p' and q' have opposite signs.
Factor pairs of (ac = -120) --> (-6, 20)(-8, 15). This sum is 7 = -b.
The opposite sum (8, -15) gives: p' = 8 and q' = -15.
Therefor, `p = (p')/a = 8/12 = 2/3` and `q = (q')/a = -15/12 = - 5/4`.
Factored form: `y = 12(x + 2/3)(x - 5/4) = (3x + 2)(4x - 5)`