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

Aug 8, 2015

Factor: $y = 6 {x}^{2} - 7 x - 5$

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

#### Explanation:

I use the new AC Method: $y = 6 \left(x - p\right) \left(x - q\right)$
Converted trinomial $y ' = {x}^{2} - 7 x - 30 =$(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. $p = \frac{p '}{a} = \frac{3}{6} = \frac{1}{2}$ and$q = - \frac{10}{6} = - \frac{5}{3}$

$y = 6 \left(x + \frac{1}{2}\right) \left(x - \frac{5}{3}\right) = \left(2 x + 1\right) \left(3 x - 5\right)$