Question

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

Answer 1

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

Explanation:

`y = 15b^2 + 32b + 16 =` 15(b + p)(b + q)
Use the new AC Method to factor trinomials (Socratic Search).
Converted trinomial: `y' = b^2 + 32b + 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 = (p')/a = 12/15 = 4/5` and `q = (q')/a = 20/15 = 4/3.`
Factored form: `y = 15(b + 4/5)(b + 4/3) = (5b + 4)(3b + 4)`