 almost finished learning all the different types of factoring techniques that we're going to use to be able to break down polynomials and analyze them and look a little deeper, right? Try to, you know, graph them and, you know, maybe start using certain types of functions in our, you know, in our models of whatever we're trying to look at, right? Now we've talked about, you know, prime factorization, factor in prime numbers, GCF, simple trinomial factor, complex trinomial factor, and differences of squares. And we just finished talking about quadratic formula, right? And inside the quadratic formula, when we're taking a look at that, we also talked about the substitution, which helps us break things down or rephrase things that we can recognize them as quadratic so we can use the quadratic formula, or use substitution to express terms in any which way we want, or use substitution to express things in a way which will help us to analyze them and break them down, right? Now the last type of factoring that we're going to talk about is called synthetic division, okay? Now, before we get into talking about synthetic division, we're going to have to talk about long division, okay? Long division, we've already sort of introduced in one video in series one, I think it's video number eight or something, where we talked about multiplication and long division. We just went through a couple of examples of how you divide things out using long division, okay? Now, I know everybody hates long division, and I'm going to try to make this session as quick as possible, but there's a saying in life where there's something that you learn when you're living your life, and the older you get, the more you get to appreciate this, or understand what the phrase really means. They say that you get to appreciate the good times a lot more when you've gone through some bad times, right? And long division, by all accounts from everything that I've heard from my students, most of my students anyway, there are some people that actually like long division, but most of my students, going through the long division, it's some serious bad times, okay? Now, what I'm going to do is try to reduce the amount of bad times that we're going to have right now, learning long division, condense that this lesson in as short of a period as possible while covering all the different information, because even though long division is a real pain for some people, for me it's just become routine, right? Some people do actually like it, but what we're going to do is try to learn, just go through the original long division, the long division with just numbers, and then see how that relates to polynomial division, dividing, doing long division with polynomials. And one thing we do need to go, one reason we do need to go into long division, is because it breaks it down for us in a way where we can actually visually see what's going on. So long division, even though it's a pain, it does have some uses in just laying out the problems for us, for us to be able to recognize what is really happening, okay? So we're just going to start with just dividing out just numbers, just integers right now, and that way we're going to get the layout of what long division looks like, and we'll see that that's exactly being mirrored when you're dividing polynomials. But long division for polynomials, it mirrors exactly the same thing as long divisions with numbers, right? So from there, we can get some of the terminology we need, and then we're going to go into synthetic division and you're going to see how sweet synthetic division is, right? And going through this right now is going to make you appreciate synthetic division a lot more, and hopefully that will help you to become really good at it, because you don't want to do long division every time. There will be times where we're going to have to do long division. That's a given, that's guaranteed. But synthetic division is what we're going to go for most of the time, okay?