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

题目无误？
x^6+2x^5+3x^4+4x^3+2x^2+2x+1
=(x^6+x^5)+(x^5+x^4)+(x^4+x^4+x^3+x^3)+x^3
+(x^3+x^2)+(x^2+x)+(x+1)
=x^5(x+1)+x^4(x+1)+2x^3(x+1)+x^2(x+1)+x(x+1)+(x+1)
=(x+1)(x^5+x^4+2x^3+x^2+x+1)
=(x+1)[x^4(x+1)+x^2(x+1)+(x+1)+x^3]
=(x+1)[(x+1)(x^4+x^2+1)+x^3]

题肯定错了原式=x^3(x^3+2x^2+3x+4+3/x+2/x^2+1/x^3)=x^3(x^3+1/x^3+2x^2+2/x^2+4+3x+3/x)=x^3[(x+1/x)(x^2-1+1/x^2)+2(x+1/x)^2+3(x+1/x)]=x^3(x+1/x)(x^2-1+1/x^2+2x+2/x+3)=x^3(x+1/x)(x^2+2+1/x^2+2x+2/x)=x^3(x...