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

Guest Mar 23, 2022

#1**0 **

x^{8} - y^{8} = (x^{4} - y^{4})(x^{4} + y^{4})

^{ }= (x^{2} - y^{2})(x^{2} + y^{2})(x^{4} + y^{4})

= (x - y)(x + y)(x^{2} + y^{2})(x^{4} + y^{4})

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.

geno3141 Mar 23, 2022