How do you factor #2x^3-162#?

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Answer 1 · 2015-07-01T11:09:57

#2x^3-162 = 2(x^3-3^4) = 2(x^3-(3^(4/3))^3)#

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

#=2(x-3root(3)(3))(x^2+3root(3)(3)x+9root(3)(9))#

Using the difference of cubes identity:

#a^3-b^3 = (a-b)(a^2+ab+b^2)#

with #a=x# and #b = 3^(4/3) = 3root(3)(3)#

I suspect a typo in the problem as stated, perhaps it should have been:

#2x^4-162#

which would factor much more nicely.