Question

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

Answer 1

Factor: `y = 6x^2 + 7x - 3`

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

Explanation:

Use the new AC Method. y = 6(x - p)(x - q)
Converted trinomial: `y' = x^2 + 7x - 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 = (p'/a) = 2/6 = 1/3` and `q' = -9/6 = -3/2`

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