To divide using long division, the X ^2 + 3 X +3 is going to go inside the box. The X + 8 is going to come on the outside. So we're going to say X times what gives us X ^2 and the answer should be X. And I'm going to line the X's up so that all the X's on on top of each other. I'm going to write X * X + 8 over here on the side just so I can visibly see what I'm doing. That's X ^2 + 8 X. If I distribute in division. Our next step is to change the signs so we could add, which is really the same thing as subtracting. So the X squareds are going to go away. We're going to get -5 X and we're going to bring down the next term. So now we want to think about X here times what gives us a negative 5X. And our answer should be -5 we're going to put that up here at the top. We're also going to put it over here on the side with that X + 8. So I can see that really all I'm doing is the distributive property -5 X -40. The next step in division is to change the signs so we can add. That's really the same thing as subtracting. The five XS are going to cancel and we're going to get 43. We have nothing to bring down, and X times something can't give us 43 because 43 has got a smaller degree than the X + 8, so that portions are remainder. So plus 43 / X + 8. So the X -, 5 is the quotient, the remainder is 43 / X + 8.