Question

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

Answer 1

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)`