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

1 Answer
Apr 21, 2016

(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)#