Okay, so Austin asked a very great question. Not that Austin, the Austin in the last row asked a great question. T squared plus 8T plus 12. The question asks, well he didn't ask a question so he knows it's not him.
Huh? Yeah. So what we look at here is With this, we have t squared plus 8t plus 12. All right?
What we're going to do is, it says factoring. And what we previously factored on factoring, like I already talked about, we took a number, okay, and we broke it down into its prime factors, right? And then last time we did it, we took a factor, and we broke it down into a product of two factors, right? That was by distributive property.
So remember, ladies and gentlemen, when I say factor, what I mean is write it as a product of its factors. So we look at this and we say, what? goes into all of these and you might say well one yes what goes into besides one or other so is there any other number or term well we have stuck with T though because the 12 nothing right they don't have a GCF that we can factor out you always want to look did you you can pull out a GCF in this problem we don't have a GCF so well we can still factor it right because factoring just means writing it as a product of its factors.
So what is a number that divides into this? Or what is a term that divides into it? Yes?
No, well, you can't combine them because this is t squared and this is to the t power. Okay? So you can't combine them because they're not like terms. Huh? 12 and 8. Nope, because that has a t as a factor and that doesn't.
So you can't combine them. So what I want to do is I want to write this as a product. And do you guys remember multiplying... Multiplying binomials?
Foil? Okay, we're going to have to go back and redo that. What I want you guys to do is this is a factor. All right?
And what we're going to do is we're going to take two binomials. Well, if we know we're going to have t times t. t times t is going to give us t squared, right? What we need to do is determine what are my last two numbers that multiply to give us 12 but add to give us 8. Okay, right, so a lot of times what I like to do, alright, this is the way I like to do it.
I like to set up a nice little x, okay, up top I write a times c, where a times c... Or a is your coefficient of t squared, which in this case is 1, and then c is my constant. So a times c is 12, and then b is 8. Okay? If you guys want to write that down, it's a very, very helpful hint to do. What two numbers do you multiply?
multiply to get to your constant, but then add to get to your middle term. Okay? So then you think. You said your last two numbers were 6 and 2, right?
So therefore, positive 6 and positive 2. Now, is this problem written as a product of a multiplication problem? Yes, right? You're not adding between these two factors. You're multiplying between the two factors.
And what I wanted you guys to do to check your work, do you guys remember how to multiply binomials? We'll have to probably review that. Multiplying binomials, remember, you can use FOIL.
First times first, which would be T times T, right? The outer, T times 2. The inner. 6 times t. And the last, which would be 6 times 2. So you get t squared, 2t, 6t, and 12, which gives you t squared plus 8t.
plus 12. So therefore, is this multiplication of this problem? Yes, it is. Okay? So yes, when you write it as a product of two binomials, it's just another way to write this.
Again, guys, while we're doing, we're not changing the problem. We are just reworking the problem, so it's now written as a multiplication problem. Okay? Well, you would think...