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

1 Answer
Nghi N.
Jul 26, 2015

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

Ans: (3x + 1)(2x - 3)

Explanation:

y = 6(x - p)(x - q)
I use the new AC Method to factor trinomials. (Google, Yahoo)
Converted #y' = x^2 - 7x - 18 = #(x - p')(x -q'). p' and q' have different signs
Factor pairs of (-18) -> (-1, 18)(-2, 9). This sum is 7 = -b.
Then, p' = 2 and q' = -9.
Then, #p = 2/6 = 1/3# and #q = -9/6 = -3/2#

factored form: #y = 6(x + 1/3)(x - 3/2) = (3x + 1)(2x - 3)#

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