Question

How do you factor the expression `9x^2 + 65x + 14`?

Answer 1

(9x + 2)(x + 7)

Explanation:

Use the new systematic AC Method to factor trinomials (Google, Yahoo).
`y = 9x^2 + 65x + 14 =`9(x + p)(x + q)
Converted trinomial: `y' = x^2 + 65 x + 126 =` (x + p')(x + q').
p' and q' have same sign, because ac > 0.
Compose factor pairs of (ac = 126) --> (2, 63). This sum is 65 = b. Then p' = 2 and q' = 63.
Back to original trinomial y, `p = (p')/a = 2/9` and `q = (q')/a = 63/9 = 7`.
Factored form `y = 9(x + 2/9)(x + 7) = (9x + 2)(x + 7)`