 Hello everyone. Today we are going to discuss just a few things about how to solve quadratics. So this first video will explain how you can solve quadratics by factoring. You should all have a sheet printed out so that you can kind of follow along with the examples. And each one will have a couple other examples that we don't get to that I want you to make sure to do for class. So first we need to factor the expression. Anytime you're solving by factoring the equation must be equal to zero. In this case it already is and so we're all taken care of in that regard. So we just need to go about factoring x cubed plus 6x squared. And here it's not a full quadratic so instead what we'll do is just factor out the greatest common factor. Notice that each of these terms has an x squared inside of it so we'll factor out an x squared. And when we take away an x squared from each piece we're left with x plus 6. So when you're solving an equation by factoring once it's factored because you're multiplying two things or sometimes more than two things and you want them to multiply to equal zero you know that at least one of these two things must be equal to zero for them to multiply to give you zero. So what we have to do is we just have to solve when each factor is equal to zero. Here when does x squared equal zero well we can take the square root of each side and the square root of zero is just zero. In the second one when does x plus 6 equal zero well we can subtract 6 from each side and we get x equals negative 6. So this expression has two solutions x equals zero and x equals negative 6. Now you also can solve quadratics by factoring. So you'll have to know how to factor which we've talked about earlier in class. Here the leading coefficient is just one so to factor this expression we just have to look at this 12. We need two things that multiply to 12 but they have to add up to a negative 8. So let's see what two things would work in this case. I think the number is negative 6 and negative 2. We'll do it for us. And so our two factors of this expression will be x minus 6 and x minus 2. One thing I should note is notice this was already equal to zero so I didn't have to do any extra work. I could just factor it right away. If it hadn't been equal to zero I just would slide things over to the other side so that everything was set equal to zero. But now that I've factored the expression now I can just find when each factor is equal to zero. So I have two equations to solve. When does x minus 6 equal zero and when does x minus 2 equal zero? x minus 6 is equal to zero when x equals 6 and x minus 2 is equal to zero when x equals 2. And so the two solutions to this equation are x equals 6 and x equals 2. That's just a basic review of solving quadratics by factoring. I hope that...