factoring

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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.

Guest Jan 15, 2021

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Best Answer

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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

Guest Jan 15, 2021

1⁺⁰ Answers

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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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