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)

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