Question

How do you factor the trinomial `12p^2-22p-20`?

Answer 1

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

Explanation:

`f(x) = 2y = 2(6x^2 - 11x - 10)`
Factor y, the trinomial in parentheses, by the new AC Method (Socratic Search).
`y = 6x^2 - 11x - 10 =` 6(x + p)(x + q)
Converted trinomial: `y' = x^2 - 11x - 60 =` (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = -60) --> ...(-4, 15)(4, -15)> This last sum is
(-11 = b). Then, p' = 4 and q' = -15.
Back to original trinomial y -->`p = (p')/a = 4/6 = 2/3`, and `q = (q')/a = - 15/6 = -5/2`
Factored form `y = 6(x + 2/3)(x - 5/2) = (3x + 2)(2x - 5)`
Factored form f(x) = 2y = 2(3x + 2)(2x - 5)