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将X^7+1因式分解

2020-01-30

将X^7+1因式分解

优质解答

x^7+1
=x^7-x^3+x^3+1
=x^3(x^2+1)(x+1)(x-1)+(x+1)(x^2-x+1)
=(x+1)[x^3(x^2+1)(x-1)+(x^2-x+1)]
=(x+1)(x^6-x^5+x^4-x^3+x^2-x+1)