 This video is called the greatest common factor. This video has four examples in it and in all four examples we're going to look at finding the greatest common factor for the polynomial. It's important to remember the greatest common factor is simply you're trying to factor out or think of dividing out things that are in all of the terms. So in this case we want to see what can I take out of here, here, and here to make my problem or my polynomial simpler. So think of it as division or think of it as factoring. Think of it as taking things out but the key is that what you take out comes out of each term. There are many ways to solve problems like this. You just have to find one that works for you. I'll show you a couple of different ways as we go through these videos. And keep in mind in problems like this we've got numbers. So we want to see what comes out of the 4, 12, and 8 and we also have letters. We want to see how many x's we can pull out as well. Let's start with 4x to the third. 4 can be broken down to 2 and 2 and x to the third can be x, x, and x. 12 can be broken down to 2, 2 and 3. 2 times 2 is 4, 4 times 3 is 12, and x squared is x and x. The negative 8 will have a negative and the negative 8 is 2, 2 and 2. 2 times 2 is 4, 4 times 2 is 8, and this case just has 1x. So then what you're doing is to see what do all three terms have in common that we can pull out. I see all three terms have a 2 so I can pull out a 2. All three terms have an x so I can pull out an x. Oh and I see all three terms have another set of 2's so another 2 can come out. I don't think there's anything in all three lists that can come out. So 2 times x times 2 is 4x. So 4x will be your greatest common factor. So that's one way to solve this problem. Another way you could solve this problem is simply ask yourself what number can divide out of 4, 12, and 8? And hopefully you can recognize that you can divide a 4 out evenly from all of those terms. So we'll take out a 4. And then remember that x to the third is really x, x, and x. x squared you have 2 of them and then negative 8x you only have 1. There's an x in all three lists so you can take out a 4x. So matter what method you choose it really doesn't matter as long as there's one that you understand. Let's try another problem. This one 4b to the third minus 2b squared minus 6b. Again there's three terms and we want to see what can come out of all three. We'll have to look at the numbers 4, 2, and 6 and also at the letters. b to the third, b squared, and b. It helps me a lot. b to the third to write it out, b squared to write it out, and b to write it out. And then the method I like to use is just ask myself what can divide out or factor out a 4, 2, and 6? If you guessed a 2 you got it right because these will all divide out evenly. So I can take out a 2. How many b's can I take out? I have 1b, 1b, 1b. Can I pull out a b again? I can't because if I tried to do that I'd find I could pull out a b from here, a b from here, but I don't have any more from this chunk to take out so I can't take any more. So 2b would be my greatest common factor. Let's try another example. This one only has two terms, a 5b to the fifth and a 10b to the third. So what I like to do is start, v to the fifth, 1, 2, 3, 4, 5 v's, and v to the third, there's three of them, and then ask what number, what's the biggest number that could divide out from a 5 and a 10 evenly? Well it'd be a 5. So I'm going to take out a 5 and then figure out how many v's I can take out. 1 pair, 2 pairs, and a third pair. So, oops, excuse me, so that would, whoa, that would be 5v to the third. One more. 3t squared minus 18. Well this one, notice, 3t squared has a number and a variable, but 18 only has a number. So, when I pull out my t's, this group doesn't have any to come out, so there's nothing I can do there, but notice, the biggest number that can divide out evenly from a 3 and an 18 is a 3. So my greatest common factor is 3.