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

1 Answer
Mar 11, 2016

(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)