Question

How do you factor the expression `6x^2 + 7x - 20`?

Answer 1

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

Explanation:

Use the new systematic, non-guessing AC Method (Socratic Search).
`y = 6x^2 + 7x - 20 =`6(x + p)(x + q)
Converted trinomial `y' = x^2 + 7x - 120 =`(x + p')(x + q').
Find p' and q' that have opposite signs since ac < 0.
Factor pairs of (ac = -120) --> (-6, 20)(-8, 15). This sum is (7 = b).
Then, p' = -8 and q' = 15.
Back to y --> `p = (p')/a = -8/6 = -4/3` and `q = (q')/a = 15/6 = 5/2.`
Factored form:
`y = 6(x - 4/3)(x + 5/2) = (3x - 4)(2x + 5)`