 This video is called, Solve by Factoring 1. Notice it's not a trinomial anymore. This is just a binomial because we have two terms. So the factoring is basically limited to pulling out a GCF, seeing what's left, and then making sure we take all our parts and solve them, set them equal to 0 and solve. So, looking at this, what number, what's the biggest number that can divide out of both 2 and 10? It would be a 2. X squared is 2x's and this 10x is just 1, so I have one pair of x's that can come out. Now in my parentheses, since I started off with two terms, I need two placeholders. Don't forget to bring down the equals 0. That's a really common mistake a lot of students make. They forget that when the instructions say solve, you need the equals 0. Okay, what comes next? 2x times what gets me back to 2x squared? Well, 2 times 1 gets me back to 2, x times x gets me back to x squared. 2 times what gets me back to 10? Well, it'll be a plus 5, and x times what gets me back to x? I've already got enough, so that part's done. I've taken out a GCF, I've filled in what's left. Now if the instruction simply said to factor, we'd be done and that would be our answer. But since the instructions say solve by factoring, we've got this equals 0 sitting out on the end, so I have to now take my two different terms and set them equal to 0. 2x equals 0 and x plus 5 equals 0. Well, 2x equals 0, since the 2 is multiplying the x, I'll divide both sides by 2. 0 divided by anything is always just 0. Subtracts 5, subtract 5, x equals negative 5. So if we were going to graph this parabola, and I know it's a parabola or a u-shape because of the x squared, I know, I don't know exactly what it looks like, but I know at 0 and at negative 5 it's going to cross the x-axis. So again, it's just a crude sketch, but it's starting to give me some idea of what my graph would look like. Let's try another one. This one, again, I know it's a parabola because I've got the x squared, so it's going to be some sort of a u-shape. And since it says to solve by factoring, I'm trying to figure out where this parabola crosses the x-axis. It's not a trinomial, it's just a binomial because there's only two terms. They're all on the right-hand side of the equal. You could rewrite this if you'd feel more comfortable, rewrite it as 4x squared minus 48x equals 0. As long as all the terms are on one side of the equal, it doesn't matter if it's the left or if it's the right. I just think this is kind of more what you're used to seeing. So since it's a binomial, the best we can do is take out a GCF, fill in what's left, and then take all the pieces and set them equal to 0. So ask yourself, what's the biggest number that can divide out of a 4 and a 48, and it would be 4? How many x's can come out? The x squared has two of them. The 48x just has one, so I have one pair of x's to come out. Now it's time to fill in the rest. Do not forget to bring down the equals 0 because that's just a reminder that you have to have equations. You have to solve them because it says solve by factoring. So let's see, where are we? Filling in what's left, 4 times 1 gets me back to 4. 4 times 1 gets me back to 4. How many x's do I need? x times what gets me back to x squared? It'll be another x, because remember there's really a 1, really a 1. 1 plus 1 gets me to 2. 4 times what gets me back to a negative 48? It will be a negative 12. I've got an x. Do I need any more here to get back to my x? No, so it'll just simply be x minus 12. So now that I have this term and this one, I have to set them both equal to 0. 4x equals 0 and x minus 12 equals 0. Well, 4x equals 0. To get the x along, you divide by 4. You get x equals 0. Here you add 12 to both sides and you get x equals 12. So these are my two answers and that tells me that if I were going to graph my parabola, my u-shape curve, it would cross the x-axis at 0 and