 Hello, everyone. Today we're going to do a quick review of factoring. So this video is just going to do a very basic review of factoring out the greatest common factor and then it also will do a short review of factoring quadratics just when the leading coefficient is 1. So in our first example here, we're just looking to factor out the greatest common factor. Greatest common factor can be just a number. It could be a variable. It could be a combination of the two. But what we want to look for is look at each term separately and see if they have anything in common. In this case, notice we have a 10, we have a 4, and we have a 2 as the numbers. So when you're looking at the numbers, you want to ask if there is another number or one of those numbers that fits inside of each of them and that each one could be divided by. In this case, 10, 4, and 2 have a 2 in common. So we'll write down that 2 and that's what we'll pull out of each of them. If you look at the variables, this first term has an m squared, the second an m, the third doesn't have an m at all. So there are no variables that are in common for all three terms. So we won't factor one out at all. So here, once we factor out a 2, we put a parenthesis after it, and then we write whatever we're left with. So in this case, when we divide 10 by 2, we're left with 5 m squared. When we divide the 4m by 2, we're left with 2m. And when you divide 2 by 2, we're left with 1. And that would be our factored expression. Later on, we'll talk about how to factor a quadratic like this. In this case, that quadratic can't be factored any farther. So there's one other type of factoring out the greatest common factors that I wanted to look at. And this is similar to factoring by grouping here. It's already factored a little bit and grouped for you. But when we do factor by grouping later on, notice you sometimes get this term that is the same. In this example, both terms have a y plus 4 in them. So even though that looks a lot different than just a number or a variable that they have in common, you can factor out that entire term of y plus 4. So we'll put the y plus 4 in front, and when we factor that out, that essentially cancels it out of each of these pieces. And so just like before, when we were factoring out the 2, we put a parenthesis and write whatever we're left with. When we take the y plus 4 away from this first term, we just start left with 3y. When we take y plus 4 away from the second term, we're left with minus 5. And so our factors of this first piece will be y plus 4 times 3y minus 5. Now, sometimes we can get even some different expressions that we can factor. So one other thing that we can factor here is we can factor quadratics. And that's probably what you are more familiar with. So let's look at these few examples of factoring quadratics. These are pretty basic ones because the leading coefficient is 1 in each of these cases. The second video that I have shows you how to factor when the leading coefficient is not 1. In this case, since the leading coefficient is 1, we only have to look at this value, the c value or the constant. Here that c value is 15. Whenever we have the c value, we need to think of two numbers that multiply to the c value and then they have to add up to the coefficient of your x or your b value. So here we need two numbers that add up to 8 and they have to multiply to 15. So you can think about it, you can do some trial and error if you need to. In this case, I know that 3 times 5 is 15 and 3 plus 5 is 8. And so what happens when you have a leading coefficient of 1 is those just fill in the spots in your binomials. So we'll get x plus 3 as one of our factors and x plus 5 as a second factor. And you always can check your answer by going through and distributing, multiplying these two binomials together. And you'll notice that when you do that, you get x squared, you get plus 5x plus 3x, which gives you your 8x and then you have a plus 15. So that one will work. Okay, let's do the same idea, but just with the second example here. First, we look at our c value. So that's a negative 48. Our two numbers have to multiply to a negative 48 and they have to add up to the coefficient of our x. In this case, they will add to a negative 2. So again, if you need to do some guessing and checking, some trial and error on your calculator, you can do that. But I see negative 48, one number will have to be negative and one will have to be positive. And since this, what they're adding to is negative, the bigger number will be negative. So in this case, negative 8 and 6 work in order to multiply to negative 48 and add to negative 2. So the two factors for this quadratic will be x minus 8 and x plus 6.