 Let's do another example, just a little bit more complicated in the last one we did, and this will be a last example because the process is the same, right? It's just a four-step method. I'm going to introduce the difference of squares in there as well to get the final answer, to factor it completely, right? And again, if the thing is equal to zero, all you're doing at the end is setting each term equal to zero and solving for dx there. And we've talked a lot about this for solving equations from series 3a. And if you don't know how to do that, the one you should be doing is taking a look at those videos to figure out how to set each term equal to zero to solve for dx, right? Right now what we're concerned about is learning this technique so we can add, you know, the complex trinomial factoring, the factor complex trinomials, basically the four-step method into our arsenal, into the techniques that we know to be able to break down polynomials, factor polynomials, solve equations, right? So it'll just be one more thing that we know to use, one more tool that we have in our box to be able to, you know, deal with problems with polynomials, right? Deal with questions that come to us in the form of polynomials. So what we have right now is negative x to the fourth minus 3x squared plus 2. And remember, when it comes to factoring trinomials, right? The simple trinomial and the complex trinomial, what you need is your first term with the x, that power there has to be double the second term power, right? And they have to be, they have to be whole numbers, right? We can't have decimals up top because those are not considered to be polynomials, right? Definition of polynomials, again from series 3a, we did, you know, I think it's videos number 89 to 90 or 91 or something like this. We talked about what the definition of a polynomial is, right? So what we want to do is have that power twice as much as that one or basically this power half that power for us to be able to do it, right? So what we want, what we want to do right now is going to grab the first term, the negative five and the sign in front of the number always goes with the number. So we're going to grab the negative five and multiply by the two. So what we got right now is going to be x to the power of four minus 3x squared minus 10 and we dropped the five from the beginning, from the coefficient, from in front of the x to the power of four. And that number, whatever we multiply the numbers by, a and c replaces c. Now what we're going to do is just factor that term right there. So what I did was leave the room, make sure you leave enough room to put the negative five back in front of those terms, right? So two numbers that multiply to give you negative 10 and have to give you negative three, it'll be negative five and positive two. So we've got x squared minus five, x squared plus two. And what we're going to do is drop the five, negative five in front of those x squared terms and that's our, the first step is that, the second step is factoring it, that's our third step. We're going to bring the negative five back in, right? So we've got negative five, x squared minus five, negative five, x squared plus two. And we're going to look at both these terms and take out the GCF and dump it. So in the first one, the GCF is going to be, you know, you could take out a five, but you don't want to do that. You want to take out a negative five, right? You want to take out as much as you can from the terms to simply, you know, because that simplifies them as far as you can go, right? So what you're going to do is take out a negative five from the first one. And the second one, there is no GCF, so you're going to leave it alone. So negative five comes out and you dump it. Yeah? Yeah, when it rains, you just wash it up, that's it. I was going to do more, but I'm going to walk away. I'll finish this one and walk away. It's going to take me 30 seconds. I just got to write two more lines, that's it. For sure, I'll come back. Yeah, yeah, I'll come back with one. Does that have to mean someone to clean it up? No, no. So we've got the, what are we, yeah. People don't like chalk. We've got negative, we're going to take out the negative five, right? We're going to put it out front and dump it. So it's going to be negative five. And when you take out the negative five, there's a negative five there. The negative, when you take out a negative five from negative five, it turns into a positive, right? It's positive one. So we take out negative five from there and negative, x squared plus one. It becomes x squared plus one and the other one just stays the same. Now, we talked about this. This is that guy factored, but you haven't gone all the way yet. Because as we talked about before, any two things subtracted from each other, you can factor. So you can factor that term further because what it is, if you rewrite that, it becomes two minus x squared, right? So what you want to do is rewrite that term as two minus x squared and it becomes two things subtracted from each other and you can factor that further. So right now, what we have is x squared plus one and two minus five x squared. What we're going to do is move on to a different wall because I'm getting kicked off this wall. So we're going to move off to another wall and solve that equation, okay? So keep this in mind. I'm going to rewrite this on another wall and solve it, okay? I can't believe I've gone through it twice so far. I forgot to turn on the camera because I'm rushing through it. Kiko, working hard to teach mathematics. So what we're going to do is just set it equal to zero on solve work. The first one we can't factor anymore, that one we're going to rewrite as two minus five x squared because it looks better that way. It's the difference of squares and then we're going to take the square root of both terms, right? So right now that becomes a little bit more obvious that it's the difference of two things. So we're going to factor that and leave that one alone. So the square root of two is just going to be two. Square root of two, square root of two. Square root of five x squared, well five is a prime number so you're just going to leave it as the square root of five. It stays inside the root symbol. Square root of x squared is just going to be x so the x squared comes out as a single x, right? And again, if you don't know how to do your radicals, it's second series and you should know how to do this, right? So again, as we talked about, if you have, you know, if you don't understand a certain principle and we're just going to continue to build on it, then everything's going to collapse, right? Because you're going to get stuck here if you don't know how to deal with your radicals. So if you don't know your radicals, you definitely have to pay attention to the series two and practice that stuff, right? So what we're going to do now, all these three terms, multiply it to give you zero, we're going to use the property of zero, the very useful property of zero, where it says if you have multiple things multiplied together to give you zero, then the only way that can happen is, is if at least one of us is equal to zero. Now we don't know which one's equal to zero, so we're going to set each of them equal to zero and then solve them there, right? And we've done a lot of examples like this and again, that's from series three, right? So we're going to grab, what we're going to do is, I'm going to grab, because I don't like the negative x, right? So I'm going to grab the negative x squared five and move her over to the other side and then divide by the square root of five. That one I'm just going to grab the square root of two and take it over and then divide by negative by square root of five. And that one I'm going to grab the one and bring it over, it's just negative one. So what we've got here is x squared is equal to negative one, this one doesn't have an answer because if you take the square root of both sides, you can't have a square root of a negative number. So this one doesn't give you an answer. Over there we can divide by the square root of five so the answer over here, so x is equal to the square root of two over square root of five and over there, that one should be a negative square root. So that one is actually negative square root two when it came over because the sign changes when it comes over, so you divide over here, divide by square root of five, over there you divide by square root. So your final solution to this, that one is not going to have an answer. This one is just going to be x is equal to square root of two over the square root of five and that one is just going to be x is equal to negative square root of two over square root of five. Now, if you remember from series two, we have to rationalize the denominator, but I'm not gonna go ahead and do that right now. Cause we're running out of walls and we're getting busted, drying on walls. So we're gonna end it for today. And this is basically the factoring complex trinomials and continuing it and brought in a difference of squares. From here, when we get into the polynomials, graphing polynomials, we're gonna start graphing them, solving them, trying to figure out what the stuff means, what it's giving us. And we've talked with us before. It's just basically giving the x-intercepts, the solutions, the factors, the roots. The guy's response was, how come you do this on walls? How come you don't do it on a piece of paper? It's very strange. You just couldn't comprehend why you would do math outside on pretty colored walls with pretty chalk and have fun doing it. But that's life. I guess everyone has to walk through life in their own little form, right? So anyway, it comes up quite easy now. Simple as that?