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Factor x^8 - y^8 as the product of four polynomials of degree 1, each of which has a positive coefficient of x.

 Mar 23, 2022
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x8 - y8  =  (x4 - y4)(x4 + y4)

             =  (x2 - y2)(x2 + y2)(x4 + y4)

             =  (x - y)(x + y)(x2 + y2)(x4 + y4)

 

This is factored as the product of four polynomials but is not the product of four polynomials

of degree 1 because that is impossible.

It is possible to further factor my result if you are allowed to use imaginary factors.

 Mar 23, 2022

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