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:

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

$4b - 18/b = 6$

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

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

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

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

How do you factor 8x^2 + 6x - 98x^2 + 6x - 9?