 So we just did x squared plus 5x plus 6 is equal to 0, right? Let's do, let's change, just change it up to slightly a little bit, a little bit and see what happens with our results. We've got x squared minus 5x plus 6 is equal to 0. All I did was change the plus side to a minus side for this problem. When you're solving this, all you do is you go bracket, bracket, bracket, bracket is equal to 0. You're looking for two numbers, I multiply it to give you 6 after giving you negative 5. Negative 2 times negative 6, negative 2 times negative 3 gives you positive 6, negative 2 plus negative 3 gives you negative 5, so those are your numbers. And for this guy, all you do is you break this x squared in here. So you're going to break this into even parts in here. If this was x to the power of 4, all you would do you put x squared here and x squared here. But that's x squared, so all you're doing is you're going x and x. And what we figured out this to be is negative 2 times negative 3. And then what you would do is just set each one of these equal to 0. So x minus 2 is equal to 0, x minus 3 is equal to 0, right? And this one is just x is equal to 2 and x is equal to 3, right? Now if you want to go from here back to here, all you would do is something called FOIL, which is, I don't like the term, I don't use the term very much, which is the first two numbers multiply together FOIL. The outside numbers multiply together, the inside numbers multiply together, and the last numbers multiply together. That's FOIL, F-O-I-L, right? What I do is just do it visually. This multiplies this, multiplies this, this multiplies this, this multiplies this. Now, to go back from here to there, this is what you do, and if you end up doing this, you're going to go x times x is going to be x squared, x times negative 3 is going to be negative 3x, negative 2 times x is going to be negative 2x, and negative 2 times negative 3 is going to be 6. Now, negative 3x plus negative 2x is going to be negative 5x. I think we've covered this before, it's just straight for FOILing, we're expanding this, and that will take you back to this. Let's do a couple more questions. So what I did here was just change it up just slightly, right? Change the sign and drop the 5. Change the sign for the 6 and drop the 5 here. So again, you're going to do the same thing, you're going to go bracket, bracket. And you're going to ask yourself, what are two numbers that multiply to give you negative 6? An ad to give you, if there is no number here, is a 1. So they add to give you negative 1. Okay, again we're dealing with 2 and 3, but they have to multiply to give you negative 6, going to be negative 3 and positive 2. So it's going to work out, and this is, so it's going to be negative 3 and positive 2. Now, if you do the little table, these are the only combinations that are going to give you multiply to give you negative 6. Negative 3 times 2 is negative 6. Negative 3 plus 2 is going to give you negative 1. So if you know your multiplication, this stuff should come fairly easy. If you don't know your multiplication table, then it's going to take a little bit of effort to do this, to get to this. And in general, initially this is a little bit hard for people to figure out what the two numbers are, and I'm using really simple numbers here. Later on we might do some problems with more complicated numbers, but the better you know your multiplication table, the easier this stuff will be. So learn your multiplication table, because the numbers in general you're going to get are going to be a little bit more complicated. It's just 6 and 1. Over here what you're going to do is, what goes here and here is going to be x squared. It's the square root of whatever is here. Squared of x to the power of 4, it's just going to be x squared. So what you do, again, you've got two things multiplied to give you zero. So what you do, you set each one equal to zero. So this is going to be x squared minus 3 is equal to zero, and x squared plus 2. From here all you do, you solve for these, and we know how to solve for these. You grab the 3, bring it over. So this becomes x squared is equal to positive 3. Over here you grab the 2, bring it over. So that's x squared, the negative 2. Right? Now to get the x-byte solve, you have to take the square root of bosa. So you take the square root from this side, you take the square root from this side. Square root, square root. Now over here we have no answer because we're taking the square root of a negative number, right? So this one doesn't give us any solutions. This branch of the answer, right? So no solutions here. Over here, square root of x squared is just x. Square root of 3 is, this thing is going to give you two solutions. It's going to be positive square root 3 and negative square root 3. So the answer for this guy is going to be, let's do this, we're going to write this. But for this guy, it's just going to be x is equal to plus or minus square root of 3, okay? And that's the solution to this because this branch didn't give us any solutions. It's the square root of a negative number. And again, this thing does have answers. They're called complex numbers or imaginary numbers. But we're not dealing with these right now. We will later on hopefully get into them much, much later. And hopefully in a couple of years maybe. So problem where we're doing a combination of GCF and simple trinomial factoring, which is what we've been doing for the last three or four problems, right? This thing, now we have a problem with because we can't factor the simple trinomial factor is not going to work because we don't have x for simple trinomial factor. We need this power to be half power of this guy. So this thing's not going to work. So again, what we're going to try to do is take out a GCF from this. And again, this is going to be for every type of problem, every type of equation you get, you're always going to look for a GCF. So first thing we're going to do when we're trying to solve this problem, we're going to take out the GCF and once we take out the GCF, we're going to have a simple trinomial factor that right away. So again, whenever you're encountering problems solving any type of equation, the first thing you should be looking for is a GCF and from this we do have a GCF. We have 3, 3, and 18. So we can take out a 3 from all three terms and we have an x to the power of 5. The smallest factor from all three of them, right? The weakest link in the chain we can take out. So what we have here is we're going to end up having 3x coming out and what we have left here is going to be x to the power of 4 minus we've got 3x coming out. So we just need an x squared here minus we took a 3 out of 18. So there's going to be a 6 left and we already took out the x. So we don't need anything. We don't need an x. So that's going to be like this. All right. And this guy is the same problem we had as the last one. So we already know what the answer to this question is. We just happen to have an extra solution here. So we have two things multiplied together that give us 0. So what we're going to end up doing is setting each one of these things equal to 0. Right? So this guy's going to be 3x is equal to 0. This guy's going to be x to the power of 4 minus x squared minus 6 is equal to 0. And we already solved for that one. We already know what the answer to this one is. I'm not going to bother solving for it. This one is going to give us the solution is x is equal to 3 plus and minus square root of 3. We get two solutions out of that one and for this one you just divide by 3. So it's just x is equal to 0. And this question here is giving us or this question here has given us three solutions. x is equal to 0. x is equal to positive square root 3. x is equal to negative square root 3. And those, again, are your x intercepts for, now this is no longer a quadratic equation. This is an equation to the power of 5, right? Or a function to the power of 5. So that means it has five different curves in it. And again we'll get into analyzing these functions much later when we're doing functions. Okay? But right now all we're concerned with is solving for them because it's one of the main things that we do when we have equations, right? We solve for equations, which basically means finding the x intercepts.