 This video will talk about the box method. So the problem that we're gonna do is the x is the positive 5 1. We did this in the last video. I just want to show you the difference between AC method and box method and then you can choose which way you like. Greatest common factor. No, we don't have any. AC was 10, B was 11 and we actually already know that M is 1 and N is or 10 and 1 are my M and N. So when you do the box method, it's kind of like a tic-tac-toe. Okay, and we're never going to use this box right here. That one never gets used. But what happens is you put your first term in this box and you put your last term in this box and then you put your M and N in these boxes. So what does that look like? My first term is 2x squared. It always gets that middle box and then diagonally down from that one is going to be our 5, which is our last term. And then the M and N that we found from our x go in here and it doesn't matter which one goes where. I'm going to put 10x and 1x, but you might put 10 here and 1 there. That would be okay, too. They just have to be diagonal from each other. So then what we're going to do is find the greatest common factor in this row. So that this is step one after we filled it in. Greatest common factor between 2x and 2x squared and 10x would be 2x. And now we're going to find the greatest common factor going this way. And if we find the greatest common factor there, 2x squared and x, they just have x in common. Now double check. 2x times x, that's 2x squared. So we're good. Now we have to find the other factors. But we have 2x that we're multiplying here. So 2x times what can I put up here that will give me 10x? Well, it's a positive 10 times 2x will give you not 10. Well, it's a positive 5 times 2x will give you 10x. And then we look here and we say, okay, well, at this time, I know that this x going this direction, what do I have to multiply to get to 1x? That will fill in my last box. And that would be a positive 1. And then we want to come in here and check. Okay, we want to check and make sure that these two things, 1 and 5, really do give me 5. And once I'm done with that, then we can come back and write our factors. And our factors are going to be on the outsides of the box, the purple in my case. So it factors to 2x plus 1 and x plus 5. Let's take a look at the second problem we did in factoring part 2. This time, it shows you which we did at AC method. Now we're going to do the box method. Now, I'll set up the factoring the box for you real quick. So your first term was 3t squared and your last term was 12. Remember, in the AC method, we kept those on the outsides and we filled in the middle. And so those are, they're still doing the same thing. It's really kind of like taking the box and taking the AC method and scrunching it up. So then we take our negative 4t and negative 9t. Doesn't matter which one's where, for the box, greatest common factor here that's going to give me just a t. And then we do greatest common factor here and that's going to give me a 3t. And then we do t times what will give me negative 4t and that would be minus 4. So there's one factor. And then we have 3t times what will give me negative 9t and that would be a negative 3. And then remember, we got a double check. Does negative 3 times negative 4 equal negative 12? And yes it does. So again, that 3t minus 4 was one factor. And then up and down, we had t minus 3. Same factors, just a second way to do it.