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Question: Factor the trinomial.
72x2 + 17x - 72


A ) (9x + 8)(8x - 9)
B ) (9x - 8)(8x + 9)
C ) (8x - 9)(x + 9)
D ) (x - 8)(81x + 64)

Steps to derive

2 72x2 + 17x - 72
 [Given trinomial.]

3 a = 72, b = 17, c = - 72
 [Compare with ax2 + bx + c.]

4 Find two numbers whose product is 72 and another two numbers whose product is - 72.
    Factors of 72         Factors of - 72
   1, 72 and 8, 9              - 8, 9

5 Use FOIL method to check the middle term in the trial factors.
    Trial factors           Middle term
    (x - 8)(72x + 9)     9x - 648x = - 639x
    (8x - 8)(9x + 9)     72x - 72x = 0
    (9x - 8)(8x + 9)    81x - 64x = 17x

6 So, 72x2 + 17x - 72 = (9x - 8)(8x + 9).



Hence the right answer is Option B

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