Question

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

Answer 1

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

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

Explanation:

Use the new AC Method: y = 3(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)--> (-2, 9). This sum is 7 = -b.
Change this sum to the opposite. Then p' = 2 and q' = -9.
Therefor, `p = (p')/a = 2/3` and `q = -9/3 = -3.`

`y = 3(x + 2/3)(x - 3) = (3x + 2)(x - 3)`