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How do you factor # x^6 + 16x^3 + 64#?

1 Answer

Konstantinos Michailidis

Mar 12, 2016

We have that

# x^6 + 16x^3 + 64=(x^3)^2+2*8*x^3+(8)^2=(x^3+8)^2#

But #x^3+8# can be factored further as follows

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

Finally we get

#x^6+16x^3+64=(x+2)^2*(x^2-2x+4)^2#

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