How do you factor #6x^2-19x+15#?

1 Answer
Nghi N.
Aug 5, 2015

Factor #y = 6x^2 - 19x + 15#

Ans: (2x - 3)(3x - 5)

Explanation:

#y = 6x^2 - 19x + 15 =# 6(x - p)(x - q).
I use the new AC Method to factor trinomials. (Google, Yahoo, Bing Search)
Converted trinomial #y' = x^2 - 19x + 90 = #(x - p')(x - q').
Factor pairs of 90 --> ...(6, 15)(9, 10). This sum is 19 = -b. Then p' = -9 and q' = -10
Therefor, #p = (p')/a = -9/6 = -3/2# and #q = -10/6 = -5/3#
Factored form # y = 6(x - 3/2)(x - 5/3) = (2x - 3)(3x - 5)#

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