# How do you factor -63x^2 - 19x + 30?

May 28, 2015

y = -(63x^2 + 19x - 30 = (x - p)(x - q).
I use the new AC Method to factor trinomials (Google, Yahoo Search).
Convert y to $y ' = {x}^{2} + 19 x - 1890$= (x - p')(x - q').
p' and q' have different signs (Rule of Signs). Compose factor pairs of (a.c = -1890) and find the pair whose sum is b.
Use a calculator and start from the middle:...(-30, 63)(-35, 54). This sum is (54 - 35 = 19 = b). Then, p' = -35 and q' = 54.

Back to y,$p = \frac{p '}{a} = - \frac{35}{63} = - \frac{5}{9}$, and $q = \frac{o '}{a} = \frac{54}{63} = \frac{6}{7}$

Factored form: y = -[(x - 5/9)(x + 6/7)] = -[(9x - 5)(7x + 6)]

Check by developing:$y = - \left(63 {x}^{2} + 54 x - 35 x - 30\right)$ OK

NOTE . The new AC Method is fast, systematic, no guessing, no factoring by grouping, and no solving binomials.