Question

Can `y=2x^2+9x-5` be factored? If so what are the factors ?

Answer 1

(2x - 1)(x + 5)

Explanation:

`y = 2x^2 + 9x - 5 =`2(x + p)(x + q)
Converted trinomial `y' = x^2 + 9x - 10 =` (x + p')(x + q').
p' and q' have opposite signs. Factor pairs of (-10) --> (-1, 10). This sum is 9 = b. Then p' = -1 and q = 10.
Back to y, `p = -1/2` and q = 10/2 = 5
`y = 2(x - 1/2)(x + 5) = (2x - 1)(x + 5)`