How do you factor #18x^2 -15x - 18#?

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Answer 1 · 2017-02-12T00:15:52

#18x^2-15x-18 = 3(3x+2)(2x-3)#

First separate out the common scalar factor #3#, then use an AC method...

#18x^2-15x-18 = 3(6x^2-5x-6)#

To factor #6x^2-5x-6# first look for a pair of factors of #AC = 6*6 = 36# which differ by #B=5#.

The pair #9, 4# works.

Use this pair to split the middle term and factor by grouping:

#6x^2-5x-6 = (6x^2-9x)+(4x-6)#

#color(white)(6x^2-5x-6) = 3x(2x-3)+2(2x-3)#

#color(white)(6x^2-5x-6) = (3x+2)(2x-3)#

Putting it all together:

#18x^2-15x-18 = 3(3x+2)(2x-3)#