[tex]x^6 - x^5 - 7x^4 + x^3 + 6x^2=\\x^2(x^4-x^3-7x^2+x+6)=\\x^2(x^4-x^3-7x^2+7x-6x+6)=\\x^2(x^3(x-1)-7x(x-1)-6(x-1))=\\x^2(x-1)(x^3-7x-6)=\\x^2(x-1)(x^3-9x+2x-6)=\\x^2(x-1)(x(x^2-9)+2(x-3))=\\x^2(x-1)(x(x-3)(x+3)+2(x-3))=\\x^2(x-1)(x-3)(x(x+3)+2)=\\x^2(x-1)(x-3)(x^2+3x+2)=\\x^2(x-1)(x-3)(x^2+x+2x+2)=\\x^2(x-1)(x-3)(x(x+1)+2(x+1))=\\x^2(x-1)(x-3)(x+2)(x+1)[/tex]