[tex]x^{5}+ x^{4}+ x^{3} + x^{2} +x+1 =\\\\=x^ 4 (x + 1) + x^{2} (x+1) +(x+1)=\\\\=(x+1)(x^4+x^2+1)[/tex]
[tex](x+1)[ x^4-x+ x^2+x+1] =\\\\=(x+1)[x(x^3-1)+ (x^2+x+1)]=\\\\=(x+1)[x(x-1)(x^2+x+1)+(x^2+x+1)]=\\\\=(x+1)[(x^2+x+1)(x (x-1)+1) ]=\\\\=(x+1) (x^2+x+1)(x ^2-x+1)[/tex]
