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

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Answer 1 · 2016-03-12T19:13:52

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

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

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