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

Aug 9, 2015

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

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

Explanation:

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

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