Question

How do you factor the trinomial `30r^2-19r-63`?

Answer 1

y = (6x + 7)(5x - 9)

Explanation:

I use the systematic, non-guessing, new AC Method to factor trinomials (Nghi Nguyen, Google, Yahoo Search))
`y = 30 x^2 - 19x - 63 =` 30(x + p)(x + q)
Converted trinomial: `y' = x^2 - 19 x - 1890 =` (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
Compose factor pairs of (ac = -1890) by using a calculator --> ...(-30, 63)(-35, 54). This sum is (54 - 35 = 19 = -b). Then, the opposite sum (35, - 54) gives: p' = 35 and q' = -54.
Back to original trinomial: `p = (p')/a = 35/30 = 7/6` and `q = (q')/a = -54/30 = - 9/5.`
Factored form: `y = 30(x + 7/6)(x - 9/5) = (6x + 7)(5x - 9).`