Question

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

Answer 1

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`