Question

How do you factor the expression `3x^2+7x-6`?

Answer 1

(3x - 2)(x + 3)

Explanation:

Use the systematic new AC Method to factor trinomials (Socratic Search)
`y = 3x^2 + 7x - 6 =` 3(x + p)(x + q)
Converted trinomial: `y' = x^2 + 7x - 18 =`(x + p')(x + q').
p' and q' have opposite signs.
Factor pairs of (ac = -18) --> (-2, 9). This sum is 7 = b. Then p' = -2 and q' = 9. Therefor, `p = (p')/a = -2/3` and `q = (q')/a = 9/3 = 3.`
Factored form: y = 3(x - 2/3)(x + 3) = (3x - 2)(x + 3)