How do you factor #3x^2-7x-6#?

1 Answer
Nghi N.
Aug 9, 2015

Factor: #y = 3x^2 - 7x - 6#

Ans: (3x + 2)(x - 3).

Explanation:

Use the new AC Method: y = 3(x - p)(x - q)
Converted trinomial: #y' = x^2 - 7x - 18 =# (x - p')(x - q')
p' and q' have opposite signs. (Rule of signs)
Factor pairs of (-18)--> (-2, 9). This sum is 7 = -b.
Change this sum to the opposite. Then p' = 2 and q' = -9.
Therefor, #p = (p')/a = 2/3# and #q = -9/3 = -3.#

#y = 3(x + 2/3)(x - 3) = (3x + 2)(x - 3)#

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