Question

How do you factor the trinomial `2x^2 + 17x - 9`?

Answer 1

(2x - 1)(x + 9)

Explanation:

Use the new AC Method (Socratic Search).
`y = 2x^2 + 17x - 9 =` 2(x + p)(x + q)
Converted trinomial `y' = x^2 + 17x - 18 =` (x + p')(x + q').
Since a + b + c = 0, use shortcut. p' = -1 and q' = 18.
Back toy,`p = (p')/a = -1/2`and `q = (q')/a = 18/2 = 9`.
Factored form:
`y = 2(x - 1/2)(x + 9) = (2x - 1)(x + 9)`