 and welcome back. When I was doing my polynomial long division and my synthetic division videos I realized that you really couldn't compare the two so I'm just going to do a quick video of using my old polynomial long division example and using synthetic division to actually do that example also. So my polynomial long division example was almost a 10 minute video. I don't remember the exact number for it but it was something around there. So it took me a while to explain it and it does take a while for these to be done. Notice here that I mean there's a lot of numbers, there's a lot of dividing, there's a lot of stuff you have to do here and a lot of stuff you got to keep track of. And now what I'm going to do is I'm going to show this, we've already seen, I've already done the video on the long division part of this. Now I'm just going to show you the synthetic division part. So over here on the right side I'm going to show the synthetic division. So I'm going to show you how quickly and how easily you can use synthetic division to solve these. Actually just giving more props to synthetic division and how great the process actually is. So here we go. So what I'm going to do inside this box if you remember some from synthetic division is going to go what we're dividing by, is going to go this number here but we're actually going to make it positive. So in this case it's going to be a positive 3. Now what I'm going to do is I'm going to write all my coefficients here, all my coefficients and if there's any gaps I need to write a 0 in there. So I'm going to look at here, actually you know what I'm going to rewrite this. So we can see this a little bit better. 2y to the third minus y squared plus 0y, there's my gap. I don't have a y in here, okay, plus 25. Don't forget that gap. Now I'm just going to write the coefficients of 2, negative 1, 0 and a positive 25. Now actually what I need to do is I need to scoot these numbers over just a little bit because the 25 needs to be right over this box over here because if you remember from the synthetic division video this box right here gives us the remainder of this problem. So anyway, now we just kind of start the process. Take this 2, I'm going to bring it down. 3 times 2 is 6, I'm going to bring that up here. Then add down to get 5. 3 times 5 is 15, add this down to get another 15. 3 times 15 is 45, add these together to get 70. That's actually how quick the process is as long as you can set it up. Again, remember it's just add down, multiply up. Again, we multiply by this number that's over here in the box. This number comes from the opposite of what we're dividing by. So here we go. Now what I need to do is I need to write out the answer. Now I'm going to do this a little bit differently from my synthetic division video. I'm actually going to write it from forward to backwards. I'm going to start here and write the answer and then work my way down the line, kind of opposite of what I did in the video. You can choose whichever method you like to write your answers. I'm just going to show both ways. Anyway, I know this is going to be my remainder. This is going to be constant, linear, quadratic. That tells me this is going to be 2y squared. This is going to be my plus 5y. This is going to be my plus 15. This is going to be my remainder of 70 over, what am I dividing by? Dividing by y minus 3. There we go. Notice this answer here matches up with this answer right here. It's the exact same thing. Now I just wanted to show that because I wanted to show the difference between these two processes. I wanted to show the difference between these two processes. You can decide yourself which one you like better. When I was in high school, I was of the opinion I liked long division better because I knew what this process was. I did not like synthetic division because I just didn't get it right away. But after a while, after using it on a bunch of different examples, I realized how easy and how simple and straightforward and easy. Just how easy it is. Notice that over here there's all these variables, all this junk going on over here. We just got numbers. That's it. No variables, no nothing. We start with variables at the beginning. We get rid of them. We just use coefficients. We just add down, multiply up, and then we just take our answer right here. These coefficients of our answer and we just rewrite it with the variables. It's so easy. It's so easy, so straightforward. Anyway, I just want to do a quick video on comparing the two and you guys can make the decision whether you like your long division better or if you like your synthetic division better. You can make that decision. All right, I hope you enjoyed the video and thanks for your time. Thanks for watching.