a^4+2a^3+3a^2+2a+1因式分解

分类: 作业答案 • 2021-12-19 11:02:36

问题描述：

a^4+2a^3+3a^2+2a+1
因式分解

答

a^4+2a^3+3a^2+2a+1
=a^4+2a^3+a^2+2a^2+2a+1
=a^2(a^2+2a+1)+2a(a+1)+1
=a^2(a+1)^2+2a(a+1)+1
=[a(a+1)+1]^2
=(a^2+a+1)^2