 So let's do one where it's a little bit complicated, where we actually have to take out a GCF first, right? Because again, whenever you're factoring, whenever you're trying to solve equations, the first thing you're looking for is commonality. The first thing you're trying to do is find a GCF term, right? So let's do this one. It's again, it's the same process as four steps and you know, it works out beautifully. If done, you know, if you practice it, it just goes And you know, after four steps, you should have the answer at the end. Okay, so we got 4x cubed plus 30x squared minus 34x. So the first thing we want to do is look for a GCF. Always, always, always. And obviously for the GCF, we have an x we can take out of every term and all the numbers are even so we can take out, can we take out a 4? We can't take out a 4 so we can take out a 2, right? So if you, if all your numbers are even, you can definitely take out a 2, right? And again, this comes to your multiplication table. You've got to know your multiplication table because if you know it well, as soon as you look at something like this, you know what the greatest common factor between between each term is. If you don't know it, then you're gonna have to break down each term to its prime factors and then from there, from the prime factors, you can figure out what's common between them and take it all up. Now, that becomes really hard if you've got, you know, fairly large numbers like 30 you can break down into 2x15 and 15 becomes 3x5, right? 34 becomes 2x17 and 4 becomes 2x2. So the commonality between all of them is the prime number common between all of them is just 2. If there were two prime numbers between all of them, you can take that out as well, right? So what we're gonna do, the GCF coming out of that is gonna be 2x. Take out 2x from 4x squared, you're gonna end up with 2x squared. 2 out of 30 is 15, x comes out of that becomes 15x. 2 out of 34 is 17, take the x out and it's done, right? So what you're left with is 2x times 2x squared plus 15x minus 17. Now, you can't take out the 2, you can't GCF out the 2, so this is not a simple trinomial, it's a complex trinomial. So what we're gonna do is we're gonna use our four-step method. We're gonna grab the 2, multiply it by negative 17 and drop it from the first term and whatever the multiplication is, leave it as the c term, right? That's the third term. And again, you want your, you want your terms here to be descending order of the power of x, right? So what we're end up with is 2x times x squared plus 15x minus 34. Now, keep in mind, this term does not equal that term right now because we sort of used a trick to take the 2 and multiply it by the negative 17. This term does not equal the top term. What we're gonna end up doing is factor this whole thing out and the last term is gonna be equal to the top term factor, okay? So keep this, keep this in mind if you're ever asked all the terms here equal to each other or is every line equal to each other? The answer is no. The top term and the last term is gonna be equal to each other. The second term for sure is equal to that, right? So what we're gonna do is end up factoring that as a simple trinomial. Two numbers that multiply to give you negative 34 add to give you 15. That's gonna be positive 17 and negative 2, right? It's because positive times negative gives you negative. And again, you're starting with this and if you're having a hard time just factoring simple trinomial, take a look at the simple trinomial videos, okay? Because I'm not gonna go through how to factor simple trinomials. We've moved on into complex trinomials, right? Everything in mathematics builds on top of everything else, right? So, you know, we build a base and put it on top, put it on top, put it on top. That's why math should literally be the easiest course you ever take in your life because what it does is, you know, everything you learn is not brand new. It's just building on something else you should have learned, right? The problem most people have with math is they, you know, they're missing something here and you can't build on, you know, a hole when you don't know what's going on. So what happens if you try to build information on top of your base there and if there is no base there, it all collapses. So people have a hard time in math because they don't know their base stuff. So really important to know your basic mathematics and build it up from the bottom up, right? Because everything else goes on top of that. So factor in negative 34 and 15 becomes 2x. And keep in mind the 2x you're not. The term here, the 2x, you're not gonna drop because that is part of the original GCF you're taking off. It's not part of the four-step method, right? The four-step method starts off as soon as you get your complex trinomial where you can't reduce it anymore, right? So step number one, multiply it out. Step number two, back to that thing out, right? Step number three, drop the two back in. Step number four, factor out whatever's inside the brackets and dump it. So we got 2x and I'm gonna leave. I always, whenever you're doing complex trinomial, here's a little hint or a little advice. Always leave a little bit of space in front of the x because what you're gonna do right now is go up here, take the two and drop it back in front of both the x terms, right? So we took the two. That's step number three. We took the two, drop it back in front of the x. Now what are we gonna do? Step number four, factor out whatever's common. Take out the greatest common factor in the brackets and dump them. For the first one, between 2x and positive 17, there is no GCF. So there's nothing we can do about it. For the other one, 2x minus 2, again, the greatest common factor is 2. So we can take out the two and dump it, right? So what we'll end up with, the final answer, this top guy factored is going to be... So the top guy factored is 2x plus 2x times 2x plus 17 times x minus 1. Now this is, if they ask you, this would be the answer if they asked you to factor this thing, right? Now if they asked you, if there was an equal sign here, if they had an equal sign... If the original question came to you that way, then all you do, we've talked about this before, right? We're gonna use the property of zero, one of the most useful properties of zero, where if you have something, things that are multiplied together to give you zero. So if you have a whole bunch of things multiplied together, equaling zero, the only way that's possible is if at least one of those things that are being multiplied together is equal to zero. So what we end up doing here is setting each term equal to zero, right? So what we're gonna do is say 2x is equal to zero, 2x plus 17 is equal to zero, and x minus 1 is equal to zero, and then we're gonna solve each term from this. So what we're gonna have is 2x is equal to zero, and to solve that one, you just divide both sides by two. So what you're gonna end up with, x is equal to zero. Over here, we got 2x plus 17 is equal to zero, so you move the 17 over, so it becomes 2x is equal to negative 17, and then divide by two. So x is equal to negative 17 over two, and for the other one, you just grab the one and bring it over, so it's x equals one, right? So what we have, what we end up having is just the difference between factoring something and solving something. All it is is just one more step, or two more steps, setting each term equal to zero and solving each term, right? And we've talked a lot about this, and you know, I'm just gonna go through the factoring style right now because once we get into solving quadratic equations, solving or solving polynomials, we're gonna do a lot of this, right? And remember, each one of these x is equal to zero, x is equal to negative 17 over two, and x is equal to one, they're your x-intercepts, right? They're your solutions, they're your roots, they're your factors.