How do you factor completely: #2x^3 - 18x#?

1 Answer
Alan P.
Jul 21, 2015

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

Explanation:

Given #2x^3-18x#

Remove the obvious common factor #(2x)#
#color(white)("XXXX")##=(2x)(x^2-9)#

Recognize the second term as the difference of squares
#color(white)("XXXX")##=(2x)(x+3)(x-3)#
#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")#Since #(x^2-a^2) = (x+a)(x-a)#

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