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

Mar 26, 2016

(9x + 2)(x + 7)

#### Explanation:

Use the new systematic AC Method to factor trinomials (Google, Yahoo).
$y = 9 {x}^{2} + 65 x + 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, $p = \frac{p '}{a} = \frac{2}{9}$ and $q = \frac{q '}{a} = \frac{63}{9} = 7$.
Factored form $y = 9 \left(x + \frac{2}{9}\right) \left(x + 7\right) = \left(9 x + 2\right) \left(x + 7\right)$