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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.

 May 22, 2022
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It is not possible because four polynomials of degree 1 can only form a degree 4 polynomial. x^8 - y^8 is degree 8.

 

However, if you factorize it, you will get x^8 - y^8 = (x^4 + y^4)(x^2 + y^2)(x + y)(x - y), which is what the question probably meant. To get this, you just repeatedly use the identity a^2 - b^2 = (a - b)(a + b).

 May 22, 2022

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