# How do you factor the expression 6x^2 -7x -10?

Feb 9, 2016

$y = \left(6 x + 5\right) \left(x - 2\right)$

#### Explanation:

I use the systematic, non-guessing, new AC Method to factor trinomials (Socratic Search)
$y = 6 {x}^{2} - 7 x - 10 =$ 6( x + p)(x + q)
Converted trinomial $y ' = {x}^{2} - 7 x - 60 =$ (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = - 60) --> (-2, 30)(-4, 15)(-5, 12). This sum is 7 = -b. Then the opposite sum of (5, -12) gives: p' = 5 and q' = -12.
Therefor, $p = \frac{p '}{a} = \frac{5}{6}$ and $q = \frac{q '}{a} = - \frac{12}{6} = - 2.$
Factored form: $y = 6 \left(x + \frac{5}{6}\right) \left(x - 2\right) = \left(6 x + 5\right) \left(x - 2\right)$