# How do you factor 15b^2 + 32b + 7 = -9?

Mar 25, 2016

(5b + 4)(3b + 4)

#### Explanation:

$y = 15 {b}^{2} + 32 b + 16 =$ 15(b + p)(b + q)
Use the new AC Method to factor trinomials (Socratic Search).
Converted trinomial: $y ' = {b}^{2} + 32 b + 240 =$(b + p')(b + q').
p' and q' have same sign because ac > 0.
Compose factor pairs of (ac = 240) -->...(10, 24)(12, 20). This last sum is (32 = b). Then, p' = 12 and q' = 20.
Back to y, $p = \frac{p '}{a} = \frac{12}{15} = \frac{4}{5}$ and $q = \frac{q '}{a} = \frac{20}{15} = \frac{4}{3.}$
Factored form: $y = 15 \left(b + \frac{4}{5}\right) \left(b + \frac{4}{3}\right) = \left(5 b + 4\right) \left(3 b + 4\right)$