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

1 Answer
Nghi N.
Sep 12, 2016

(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

Related questions
See all questions in Factorization of Quadratic Expressions
Impact of this question
1225 views around the world
You can reuse this answer
Creative Commons License