x^4-2x^3-10x^2+7x+4
问题描述：
x^4-2x^3-10x^2+7x+4
分解多项式x^4-2x^3-10x^2+7x+4后，有一因式为x^2+3x+1,分解多项式
答
x^4-2x^3-10x^2+7x+4=x^2(x^2-2x-10)+7x+4=x^2(x^2-2x+1-11)+7x+4=x^2(x-1)^2-11x^2+7x+4=x^2(x-1)^2-(11x^2-7x-4)=x^2(x-1)^2-(11x+4)(x-1)=(x-1)[x^2(x-1)-11x-4]=(x-1)[x^3-x^2-11x-4)=(x-1){x-4)(x^2+3x+1) ...