Question

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

Answer 1

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

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
`y = - (35x^2 + 9x - 18) =`-35(x + p)(x + q)
Converted trinomial: `y' = -(x^2 + 9x - 630) =` (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 = (p')/a = -21/35 = -3/5`, and
`q = (q')/a = 30/35 = 6/7.`
Factored form:
`y = -35(x - 3/5)(x + 6/7) = -(5x - 3)(7x + 6)`