How do you factor #16 - 2x^3#?

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Answer 1 · 2018-04-08T20:27:59

The fully factored polynomial is #=-2(x-2)(x^2+2x+4)#.

First, factor out the #2#:

#color(white)=16-2x^3#

#=2(8-x^3)#

Then, use the difference of cubes factoring:

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

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

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

Lastly, reorder the factors so that #x# is in the front of each one:

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

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

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

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

That's as factored as it gets. Hope this helped!