 What is the difference between Algebraic, Long Division and Synthetic Long Division? Synthetic Long Division is just a quicker way of doing this. Here, I'll show you the Synthetic Long Division, right? Check this out. Yo! First time chat. Lich! Druggan. How are you doing? I'll tune in more often. Goodbye. Goodbye. Sweet dreams, Ozzy. Take a look at the Synthetic Long Division. We'll do the same guy. I'm going to erase these guys. This is what we got with the Long Division, right? Here's what we can get with Synthetic Long Division. Want to become famous but I don't want to fly. Followers and viewers. Not really. First time chat. Jala. I have no idea what you're doing right now, but I know some math thing that might be very, very useful. I will type it in next message, okay? Hello, I'm a snake. How are you doing? Hello. Good to see you again. Which math subject should I learn to teach high school math, aside from algebra and trigonometry? Which math subjects should I learn to teach high school math? To teach high school math, you need to learn everything. So yeah, you would have to learn everything. But I would say start off with the basics first. Learn how to deal with fractions right away, ratios right away, factor polynomials. How to move around an equal sign right away, powers and all that stuff really well. That's where a lot of people have problems with initially, right? And then you've got to get into functions, graphing and stuff like that. But let's assume we wanted to do this. We wanted to do Synthetic Division on this, right? X squared plus 5x minus 7 divided by x plus 1. So what you do, you do this. Take the coefficients in front of these guys and lay them out, 1, 5, negative 7. And you're going to do it this way. And you're going to take x plus 1, and you're going to set it equal to 0 because you're assuming that might be a factor of that. And you're going to write this as x is equal to negative 1. So what you're going to do is, you're going to go x is negative 1, you're going to divide it into that. So what you're really doing is, you're subbing in, x is equal to negative 1 for x, and you're trying to find out what the remainder is. The remainder is 0, that's the remainder theorem just telling you that you're on the x-intercept. In this case, if it happens to be negative 11, that means if you sub in x is equal to 1 into this polynomial, your y is negative 11. It's a point that you just got. I'll show you how that works, right? So the way you do synthetic division, your first order is to bring this guy down, and you multiply this by this. One times negative 1 is negative 1. Add these guys up, you get 4. Bring this guy here, multiply by negative 1, becomes negative 4. Add these guys up, you get negative 11. What you have now is, this is this, 1x plus 4. So you took an x squared and divided by an x, your result is going to be 1 less x. So this part becomes x plus 4, which is that guy there. This guy is your remainder, negative 11. So what this really means is, if you have this polynomial function f of x is equal to x squared plus 5x minus 7, if you find f of negative 1, basically sub in negative 1 for x, you're going to get negative 1 squared plus 5 times negative 1 minus 7. This is going to be 1 minus 5 minus 7, which is going to be 1 minus 5 is negative 4 plus negative 7 is negative 11. So you just went, f of negative 1 is equal to negative 11. So on a grid, negative 1 and negative 11 is a point on this grid. And this is a parabola that opens up. So it's going to be looking, it's going to be like this or like that. What's the y? Just have this negative 7. Here's negative 7, 0 and negative 7. So the graph looks like this. I don't know where the vertex is. I would have to complete in the square to find the vertex on it.