When doing this kind of problem, we put X ^2 -, 4, X +8 inside the รท and X -, 3 on the outside and our question should be X times what gives me X ^2 and the answer is XI. Encourage students to line up all the XS on top of each other. Some books do this and some don't, but I think it's easier. So if I have X * X -, 3, if I do my distributive property, I can see that's really X ^2 - 3 X And when we do polynomial division, our next step is going to be sub to subtract. Sometimes we could think of that as just changing all the signs and adding so X ^2 and negative X ^2, cancel -4 X and positive 3X would give me a negative X. And then I bring down the next term. So this X over here again times what gives me negative X and our answer is -1. So I'm going to have a -1 times the X -, 3. When I distribute, I get negative X + 3. The next step is to subtract. Frequently we just change all of our signs to add. So negative X&X cancel +8 and -3 would give me +5. That +5 is my remainder, and my remainder always goes over what I was dividing by.