How do you factor the expression #6x^2 -7x -10#?

1 Answer
Feb 9, 2016

Answer:

#y = (6x + 5)(x - 2)#

Explanation:

I use the systematic, non-guessing, new AC Method to factor trinomials (Socratic Search)
#y = 6x^2 - 7x - 10 =# 6( x + p)(x + q)
Converted trinomial #y' = x^2 - 7x - 60 =# (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = - 60) --> (-2, 30)(-4, 15)(-5, 12). This sum is 7 = -b. Then the opposite sum of (5, -12) gives: p' = 5 and q' = -12.
Therefor, #p = (p')/a = 5/6# and #q = (q')/a = -12/6 = -2.#
Factored form: #y = 6(x + 5/6)(x - 2) = (6x + 5)(x - 2)#