a^15+a^14``````+a^2+a^+1 因式分解

say6002022-10-04 11:39:541条回答

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tong5777328 共回答了18个问题 | 采纳率94.4%: 设S=a^15+a^14``````+a^2+a^+1 (1)
aS=a^16+a^15``````+a^2+a (2)
(2)-(1)
(a-1)S=a^16-1
S=(a^8+1)(a^8-1)/(a-1)
=(a^8+1)(a^4+1)(a^4-1)/(a-1)
=(a^8+1)(a^4+1)(a^2+1)(a^2-1)/(a-1)
=(a^8+1)(a^4+1)(a^2+1)(a+1)(a-1)/(a-1)
=(a^8+1)(a^4+1)(a^2+1)(a+1)
a^15+a^14``````+a^2+a^+1=(a^8+1)(a^4+1)(a^2+1)(a+1); 1年前