解：x^5+x+1=x^5-x^2+x^2+x+1=x^2(x^3-1)+(x^2+x+1)=x^2(x-1)(x^2+x+1)+(x^2+x+1)=(x^3-x^2+1)(x^2+x+1)
x^5+x+1 =x^5-x^2+x^2+x+1 =x^2(x^3-1)+(x^2+x+1) =x^2(x-1)(x^2+x+1)+(x^2+x+1) =(x^2+x+1)(x^3-x^2+1)
