Question

How do you factor the trinomial `2x^2 + 9x - 5 = 0`?

Answer 1

(2x - 1)(x + 5)

Explanation:

I use the new AC Method to factor trinomials (Socratic Search)
`y = 2x^2 + 9x - 5 =` 2(x + p)(x + q) (1)
Converted trinomial `y' = x^2 + 9x - 10 =` (x + p')(x + q').
p' and q' have opposite signs because ac < 0
Factor pairs of ac = -10 --> (-1, 10). This sum = 9 = b.
Then, p' = -1 and q' = 10.
Back to trinomial (1): `p = (p')/a = -1/2` and `q = (q')/a = 10/2 = 5`

Factored form: `y = 2(x - 1/2)(x + 5) = (2x - 1)(x + 5)`