标题: [数学] 2007-11-21 [打印本页]

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作者: 老猫    时间: 2007-11-22 06:37     标题: 2007-11-21

分解因式X^8+X^6+X^4+X^2+1.

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作者: 辛苦饲养猪宝宝    时间: 2007-11-22 23:18

(x^8+x^6+x^4+x^2+1)
=(x^2-1)(x^8+x^6+x^4+x^2+1)/(x^2-1)
=(x^10-1)/(x^2-1)
=(x^5+1)(x^5-1)/(x^2-1)
=(x+1)(x^4-x^3+x^2-x+1)(x-1)(x^4+x^3+x^2+x+1)/(x^2-1)
=(x^4-x^3+x^2-x+1)(x^4+x^3+x^2+x+1).

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作者: 老猫    时间: 2007-11-23 06:35

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