Question

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

Answer 1

(7x + 1)(5x - 2)

Explanation:

Use the new AC Method (socratic Search)
`y = 35x^2 - 9x - 2 =`35(x + p)(x + q)
Converted `y' = x^2 - 9x - 70 =` (x + p')(x + q')
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = - 70) --> (-5, 14)(5, -14). This sum is -9 = b, the p' = 5 and q' = -14.
Back to y, `p = p')/a = 5/35 = 1/7`, and `q = (q')/a = -14/35 = -2/5`
Finally,
`y = 35(x + 1/7)(x - 2/5) = (7x + 1)(5x - 2)`