Question

How do you factor the expression `14m^2 + 55m + 21`?

Answer 1

(7m + 3)(2m + 7)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
`y = 14m^2 + 55m + 21 =` 14( x + p)(x + q)
Converted trinomial: `y' = m^2 + 55m + 294 =` (m + p')(m + q').
Since ac > 0, p' and q' have same sign.
Compose factor pairs of (ac = 294) -->... (3, 98)(6, 49). This last sum is (6 + 49 = 55 = b). Then, p' = 6 and q' = 49.
Back to original y, we have:`p = (p')/a = 6/14 = 3/7`, and `q = (q')/a = 49/14 = 7/2`.
Factored form:
`y = 14(m + 3/7)(m + 7/2) = (7m + 3)(2m + 7)`

NOTE : This method avoids the lengthy factoring by grouping