X-Box Method for Factoring a=1

Okay, so this video is to describe the X method Xbox method of factoring. So you're going to draw a box, you're going to draw an X and I'm going to tell you what to do with that box and that X so you get your expression or your equation. And the equation will be set equal always set equal to Y so if it's not set equal to Y, you move things around and make sure it's only equal to Y then you figure out what your coefficients are. So coefficients are the numbers in front of the variables. So there's an invisible number two. The invincible number is one. So I'm going to fill it in. One, and just a little one. So a is one. B is negative two. Get right. And C is negative three. And the next thing you're going to do is take X squared and put it in your box. X squared, the X squared term always goes up here, and the C term always goes here. You do these things without thinking, you don't have to do any tricks. You just figure out a, B, C if you put your extra, your X coord term here, you put your C term here. You don't have to do any work yet. Okay, so then what we're going to do with a and C is we're going to multiply them together and we're going to put them in the X a times C, one times negative three is negative three. And then we take our V term when we put it at the bottom of our X so negative two. And what our job is is to figure out what two numbers multiply to negative three and add to negative two. So times an ad. What number is multiplied a negative three and add to negative two? So what I do is I don't worry about the sign. Don't worry about whether it's positive or negative. I just think of numbers that multiply to three. So this number is really easy. There's only one set of numbers. But if there are more, I would make a little list for myself. So three times one. One times three. Whatever. So I'm going to put one in three here. Okay. And I don't have the signs. Yet. Now I'm going to think about what I can do to one, and what I can do to three to turn it into negative two. So if I make. The three negative. Then when I add one to it, I will get negative two. Next, you're going to add variables. So we have X in our equation. So we're going to add the variable X. Once you add the variable X, you're going to take this and this. And put them diagonally into the box you created. Okay, and you can put them in either empty spot. Doesn't matter. So one X and negative three X. And I'm going to erase my arrow, so I have some space to do things. Okay, your next step is to factor out whatever lengths for the rectangle that you can find that they have in common. So what I like to do first is do the numbers. So there's an invisible one here. So what number makes one? One times one makes one. One times what makes negative three? Well, that must be a negative three. One times what makes one. Well, that must be a one. Okay, next I'm going to do variables. What times what makes X squared? Well, that must be an X. And an X, X times X makes X squared. One X times negative three makes negative three X. X times one makes one X and one times negative three makes negative three. So I check all the boxes to make sure it gives me the numbers I need for the correct areas. So these are links. And these are areas. So this tells me that. This sum negative three X and one X make negative two X X squared. Negative three. It could also be written as a product. So this length times this length, that length being one X and remember one X can also be written without the one. So we could write it as X minus three. Times X plus one. And that's equal to Y so this is a sum, and it can be written as a product.