How do you factor #8x^2 + 6x - 9#?

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Answer 1 · 2016-07-05T21:20:45

#(4x - 3)(2x + 3) or (4x + 6)(2x-3/2)#

#8x^2 + 6x - 9#

Try # (4x + color(red)(a))(2x + color(red)(b))#

#8x^2 + (4color(red)(b) + 2color(red)(a))x + color(red)(ab)#

#implies 2a + 4b = 6# and #ab = -9#

Subbing #a = (-9)/b# into the first equation gives:

#2((-9)/b) + 4b = 6#

#4b - 18/b = 6#

#4b^2 - 18 = 6b implies 2b^2 - 3b - 9 = 0#

#b = (3+-sqrt(81))/4 = (3+-9)/4 implies b = 3 or b = -3/2#

#a = -9/b implies a = -3 or a = 6#

#(4x - 3)(2x + 3) or (4x + 6)(2x-3/2)#