Đáp án:
$(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1).$
Giải thích các bước giải:
$x^{10}+x^5+1\\ =x^{10}+x^9+x^8-x^9-x^8-x^7+x^7+x^6+x^5-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\\ =x^8(x^2+x+1)-x^7(x^2+x+1)+x^5(x^2+x+1)-x^4(x^2+x+1)+x^3(x^2+x+1)-x(x^2+x+1)+x^2+x+1\\ =(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1).$
