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](/uploads/image/z/13190583-39-3.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9Ax%5E9%2Bx%5E6%2Bx%5E3%2B1)
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)
=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)