Question

How do you factor the trinomial `12m^2 + 19m + 5`?

Answer 1

f(m) = (3m + 1)(4m + 5)

Explanation:

I use the new AC Method to factor trinomials (Socratic Search)
`f(x) = 12m^2 + 19m + 5 =` 12(m + p)(m + q)
Converted trinomial: `f'(m) = m^2 + 19m + 60` = (m + p')(m + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 60) --> (3, 20)(4, 15). This sum is 4 + 15 = 19 = b. Then p' = 4 and q' = 15.
Back to original trinomial: `p = (p')/a = 4/12 = 1/3` and `q = (q')/a = 15/ 12 = 5/4`.
Factored form: `f(m) = 12(m + 1/3)(m + 5/4) = (3m + 1)(4m + 5)`