How do you factor the expression #49x^2 + 42x + 8#?

1 Answer
Nghi N.
Jan 17, 2016

y = (7x + 2)(7x + 4).

Explanation:

I use the systematic, non guessing, new AC Method to factor trinomials (Socratic Search)
#y = 49x^2 + 42x + 8 = #49(x + p)(x + q)
Converted trinomial #y' = x^2 + 42x + 392 = #(x + p')(x + q').
p' and q' have same sign, because ac > 0.
Compose factor pairs of (ac = 392) -->...(4, 98)(8, 49)(14, 28). This sum is 14 + 28 = 42 = b. Then p' = 14 and q' = 28.
Back to original trinomial: #p = (p')/a = 14/49 = 2/7# and #q = (q')/a = 28/49 = 4/7#.
Factored form: #y = 49(x + 2/7)(x + 4/7) = (7x + 2)(7x + 4)#

NOTE. Using this new AC Method, you can avoid the lengthy factoring by grouping that is required if you factor by the existing factoring AC Method (YouTube Search)

Related questions
See all questions in Factorization of Quadratic Expressions
Impact of this question
1503 views around the world
You can reuse this answer
Creative Commons License