# How do you factor 18 - 9x - 35x^2?

Mar 19, 2016

y = -(5x - 3)(7x + 6)

#### Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
$y = - \left(35 {x}^{2} + 9 x - 18\right) =$-35(x + p)(x + q)
Converted trinomial: $y ' = - \left({x}^{2} + 9 x - 630\right) =$ (x+ p')(x + q')
p' and q' have opposite signs because ac < 0.
Compose factor pairs of (ac = -630) --> ...(-18, 35)(-21, 30). This sum is 9 = b. Then, p' = -21 and q' = 30.
Back to original trinomial: $p = \frac{p '}{a} = - \frac{21}{35} = - \frac{3}{5}$, and
$q = \frac{q '}{a} = \frac{30}{35} = \frac{6}{7.}$
Factored form:
$y = - 35 \left(x - \frac{3}{5}\right) \left(x + \frac{6}{7}\right) = - \left(5 x - 3\right) \left(7 x + 6\right)$