How do you factor # 6x^2-7x-5#?

1 Answer
Aug 8, 2015

Answer:

Factor: #y = 6x^2 - 7x - 5#

Ans: (2x + 1)(3x - 5)

Explanation:

I use the new AC Method: #y = 6(x - p)(x - q)#
Converted trinomial #y' = x^2 - 7x - 30 = #(x - p')(x - q').
p' and q' have opposite signs. (Rule of signs).
Factor pairs of -30 --> (-2, 15)(-3, 10). This sum is 7 = -b.
Change this sum to the opposite. Then, p' = 3 and q' = -10.
Therefor. #p = (p')/a = 3/6 = 1/2# and# q = -10/6 = -5/3#

#y = 6(x + 1/2)(x - 5/3) = (2x + 1)(3x - 5) #