Question

How do you factor `18b^2+15bd+2d^2`?

Answer 1

(6b + d)(3b + 2d)

Explanation:

Consider b as variable and d as a constant, and factor the trinomial by the new AC Method (Socratic Search)
`y = 18b^2 + 15db + 2d^2 =` 18(b + p)(b + q)
Converted trinomial: `y' = b^2 + 15db + 36d^2 =`(b + p')(b + q').
Find p' and q' that have same sign (ac > 0).
Compose factor pairs of (ac = 36d^2) --> (2d, 18d)(3d, 12d). This last sum is (3d + 12d = 15d = b). Then p' = 3d and q' = 12d.
Back to y, we get: `p = (p')/a = (3d)/18 = d/6`, and `q = (q')/a = (12d)/18 = (2d)/3`
Factored form:
`y = 18(b + d/6)(b + (2d)/3) = (6b + d)(3b + 2d)`