How do you factor #8x^3+4x^2-18x-9#?

1 Answer
George C.
Jun 22, 2016

#8x^3+4x^2-18x-9=(2x-3)(2x+3)(2x+1)#

Explanation:

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms. So we can factor this cubic by grouping:

#8x^3+4x^2-18x-9#

#=(8x^3+4x^2)-(18x+9)#

#=4x^2(2x+1)-9(2x+1)#

#=(4x^2-9)(2x+1)#

#=((2x)^2-3^2)(2x+1)#

#=(2x-3)(2x+3)(2x+1)#

Note that we also used the difference of squares identity:

#a^2-b^2=(a-b)(a+b)#

with #a=2x# and #b=3#

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