# Is it possible to factor y=2x^2+4x-30? If so, what are the factors?

Jan 10, 2016

y = 2(x - 3)(x + 5)

#### Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
$y = 2 {x}^{2} + 4 x - 30 =$ 2(x + p)(x + q) (1)
Converted trinomial: $y ' = {x}^{2} + 4 x - 60 =$(x + p')(x + q')
p' and q' have opposite signs because ac < 0.
Compose factor pairs of (ac = -60) --> (-4, 15)(-6, 10). This sum is
(10 - 6 = 4 = b). Then p' = -6 and q' = 10.
Back to original trinomial (1): $p = \frac{p '}{a} = - \frac{6}{2} = - 3$ and $q = \frac{q '}{a} = \frac{10}{2} = 5$
Factored form: y = 2(x - 3)(x + 5)