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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.

 Jan 15, 2021

Best Answer 

 #1
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x8-y8=(x4+y4)(x4-y4)

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

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

thus

x8-y8=(x4+y4)(x2+y2)(x+y)(x-y)

4 polynomials with positve coefficients

 

getting each to a degree of 1 is impossible,

but hey, 2 of the four have a degree of 1,

so that is not half bad

 Jan 15, 2021
 #1
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0
Best Answer

x8-y8=(x4+y4)(x4-y4)

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

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

thus

x8-y8=(x4+y4)(x2+y2)(x+y)(x-y)

4 polynomials with positve coefficients

 

getting each to a degree of 1 is impossible,

but hey, 2 of the four have a degree of 1,

so that is not half bad

Guest Jan 15, 2021

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