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

Aug 8, 2015

Factor: $y = 6 {x}^{2} + 7 x - 3$

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

#### Explanation:

Use the new AC Method. y = 6(x - p)(x - q)
Converted trinomial: $y ' = {x}^{2} + 7 x - 18$ = (x - p)(x - q)
p' and q' have opposite signs (Rule of signs).
Factor pairs of 18 --> (-1. 18)(-2, 9). This sum is 7 = -b.
Then p' = 2 and q' = -9.
Therefor, $p = \left(p \frac{'}{a}\right) = \frac{2}{6} = \frac{1}{3}$ and $q ' = - \frac{9}{6} = - \frac{3}{2}$

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