How do you factor the expression #-49x^2 - 49x - 12#?

1 Answer
Nghi N.
Jan 18, 2016

f(x) = -(7x + 3)(7x + 4)

Explanation:

I use the new systematic, no guessing, AC Method to factor trinomials (Search on Socratic)
#f(x) = -(49x^2 + 49x + 12)# = -49(x + p)(x + q).
Converted trinomial: #f'(x) = x^2 + 49x + 588 =# (x + p')(x + q').
p' and q' have same sign because ac > 0.
Use a calculator to compose factor pairs of (ac = 588) -->...(12,49)(14, 42)(21, 28). This sum is (21 + 28 = 49 = b), then, p' = 21 and q' = 28.
Back to original trinomial: #p = (p')/a = 21/49 = 3/7# and #q = (q')/a = 28/49 = 4/7#.
Factored form: f(x) = -49(x + 3/7)(x + 4/7) = -(7x + 3)(7x + 4)

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