Question

x^12+x^9+x^6+x^3+1因式分解

因式分解 快点

Answer 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

Answer 2

x^{12}+x^9+x^6+x^3+1
=(x^3-1)(x^12+x^9+x^6+x^3+1)/(x^3-1)
=(x^15-1)/(x^3-1)
=(x^5-1)(x^10+x^5+1)/(x^3-1)
=(x-1)(x^4+x^3+x^2+x+1)(x^10+x^5+1)/(x^3-1)
=(x^4+x^3+x^2+x+1)(x^11-x^10+x^6-x^5+x-1)/(x^3-1)
其中x^11-x^10+x^6-x^5+x-1
=(x^11-x^5)-(x^10-x)+(x^6-1)
=(x^6-1)(x^5+1)-x(x^9-1)
=(x^3-1)(x^3+1)(x^5+1)-x(x^3-1)(x^6+x^3+1)
=(x^3-1)[(x^8+x^5+x^3+1)-(x^7+x^4+x)]
=(x^3-1)(x^8-x^7+x^5-x^4+x^3-x+1)
∴原式=(x^4+x^3+x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1)

Answer 3

x^(12+9+6+3)+1=26x^+1