因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/05 14:51:49
因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1拆

因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1
因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1

因式分解:x^6+2x^5+3x^4+4x^3+3x^2+2x+1
拆项组合
(x^6+2x^5+x^4)+2(x^4+2x^3+x^2)+(x^2+2x+1)
=x^4(x^2+2x+1)+2x^2(x^2+2x+1)+(x^2+2x+1)
=(x^4+2x^2+1)+(x^2+2x+1)
=(x^2+1)^2 (x+1)^2