因式分解：x^9+x^6+x^3+1

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因式分解：x^9+x^6+x^3+1因式分解：x^9+x^6+x^3+1因式分解：x^9+x^6+x^3+1x^9+x^6+x^3+1=x^6(x^3+1)+x^3+1=(x^3+1)(x^6+1)=

因式分解：x^9+x^6+x^3+1
因式分解：x^9+x^6+x^3+1

因式分解：x^9+x^6+x^3+1
x^9+x^6+x^3+1
=x^6(x^3+1)+x^3+1
=(x^3+1)(x^6+1)
=(x+1)(x²-x+1)(x²+1)(x^4-x²+1)

简短点的就是：
x12+x9+x6+x3+1
=(x^15-1)/(x^3-1)
=(x^5-1)/(x-1) * (x^10-x^5+1)/(x^2+x+1)
=(x^4+x^3+x^2+x+1) * (x^8-x^7+x^5-x^4+x^3-x+1)
看不懂就给你看图，这题好像是初中的奥赛题目
以上回答你满意么？

x^9+x^6+x^3+1
=(x^9+x^6)+(x^3+1)
=x^6(x^3+1)+(x^3+1)
=(x^6+1)(x^3+1)
=[(x^2)^3+1^3](x^3+1^3)
=(x^2+1)(x^4-x^2+1)(x+1)(x^2-x+1)

x^9+x^6+x^3+1
=(x^9+x^6)+(x³+1)
=x^6(x³+1)+(x³+1)
=(x^6+1)(x³+1)
=(x²+1)(x^4-x²+1)(x+1)(x²-x+1)

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