# How do you factor #(7x^2+11x-6)/(x^2-4)#?

##### 1 Answer

Jul 21, 2016

#### Explanation:

First, factor the numerator y by the new AC Method (Socratic Search).

y = 7x^2 + 11x - 6 = 7(x + p)(x + q)

Converted trinomial y' = x^2 + 11x - 42 = (x + p')(x + q')

p' and q' have opposite signs. Factor pairs of (ac = -42) -->

(-2, 21(-3, 14). This last sum is (11 = b). Then p' = -3 and q' = 14.

Back to original trinomial y,

Factor form of y:

y = 7(x - 3/7)(x + 2) = (7x - 3)(x + 2)