1. The problem statement, all variables and given/known data Show that x^7 + 3x^6 + 3x^5 - x^3 - 3x^2 - 3x is divisible by x^5-x 2. Relevant equations 3. The attempt at a solution So i did polynomial long division and as a quotient so far I have x^2+3x, and it appears that my remainder is going to be 3(x^3-x). Does this mean that I did something wrong? I'm relooking the steps of my long division very carefully and I can't find any mistake. I mean, after doing the step involving subtraction I arrive at 3(x^3-x), and obvioulsy I can't use x^5-x to divide it anymore because it's of a greater degree. Anyone have any insight?