Question

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

Answer 1

(3x + 2)(x - 3)

Explanation:

Use the new AC Method (Socratic Search)
`y = 3x^2 - 7x - 6 =` 3(x + p)(x + q)
Converted trinomial `y' = x^2 - 7x - 18 =` (x + p')(x + q')
p' and q' have opposite signs because ac < 0.
Find p' and q' knowing their sum (-7) and their product (-18). They are: p' = 2 and q' = -9.
Back to y, --> `p = (p')/a = 2/3` and `q = (q')/a = -9/3 = -3`
Factored form:
`y = 3(x + 2/3)(x - 3) = (3x + 2)(x - 3)`