 Hi, this is Chico again. Now as I previously mentioned, what we're going to do now is learn a new technique of solving equations, quadratic equations, which are basically more complicated equations, one order of magnitude, more complicated than just a linear equation, linear function. Now we'll get into all that stuff and what they all mean later on, we'll go into coordinate geometry and we'll talk about more about functions. What we're concerned about in these next few videos is learning the techniques of factoring. As I previously mentioned, there's four different types of factoring. There's a GCF, which is greatest common factor. There's a simple trinomial factor, difference of squares and complex trinomial factor. I used a four step method for that, but we'll get into that. The reason we're learning all these four different techniques is basically because all of our equations are not just going to be simple equations where we can move around an equal sign just using the simple rules that we learned and be able to isolate our x on one side with equaling to a number or other variables. We're going to get more complicated equations. We're going to start dealing with more complicated functions. The first thing we have to do is learn how to solve these more advanced problems, more advanced functions. The first method, which is a general rule that you're going to end up using whenever you see whatever types of equations you come across, which is called the greatest common factor. Whenever you see an equation, what you're going to try to do is take out a GCF right away. GCF basically refers to trying to find a pattern within different terms. If you're given a multivariable term, multivariable equation or a function, what you're going to try to do is find out what's similar between each one of those terms and take it out of the equation and put it in the front. For example, if you had something like, you know, if we go back to our prime numbers, let's talk about our prime numbers for a second, right? For example, if you had, let's do, let's do porch. Four, four and six. Let's say you had four plus six. Now if you had this, you would just add these up and this equals 10, right? But one thing you can do with these is break these down to their prime numbers. So four would be two times two. Six would be two times three, right? So what's similar between four and six is they both contain a two. So what you can do is, instead of writing four plus six equals 10, what you can do is take out this two for both of these terms. So whatever's similar between them, you can take it out to the front. So what you can do is take out a two from this and if you take out a two from this, you can take out a two from this and when you take it out, it comes to the front of the equation. So that becomes two. What's left here is two and a three and if they're added together, right? So what you do is you go two plus three is equal to 10, right? So two plus three is five times two is 10. That's the same thing as six. Four plus six is 10, right? This is the basic principle. This is the basic idea of doing a GCF, taking out a GCF from an equation, okay? Now obviously we wouldn't bother doing this with something as simple, but what would happen if you had, for example, let's say an A here and a B here, right? Now you could just simply go four A plus six B. You can't add those. So what you would do is take out the two from both of them and this would be two A plus three B, right? Now this may seem silly to do, but this is something that we're going to end up doing to be able to solve equations because we're going to use the property of zero where it says if you're trying to, you know, if you have multiple things multiplied together, for example, two things multiplied together to give you zero, then all you do is set each one equal to zero. We've talked about this before, right? So let's go find another wall and we'll just move down a little bit and do another problem where, you know, we're going to slowly mutate this thing, morph this thing into something more recognizable. So, you know, it becomes more clear of why we end up doing this.