10.2C Factor tromials with the greatest common factor. We should always factor the GCF first. Since we've started factoring, you have had a couple of things that we've done. We've done the GCF where we've just had that. We've factored by grouping. And then we factor by trial and error or the reverse foil. Okay. Now, we're going to add greatest common factor back in with our trial and error. So, we want to get in the habit of when we look at a tromial, we'll always want to look for a common factor before we do anything else. So in example one here, if I look at my numbers, I have an 18, 21, and 15. And I notice that that means that we have a common factor of three. I notice that they all have a factor of x. And my lowest exponent for my x is two. So that means my GCF is 3x^2. So we're going to take 18 / 3 which should give us 6 x^2 or x 4 / x^2 which gives me x^2 my minus 21 / 3 is 7 x cub / x^2 is x another minus 15 / 3 is 5 and x^2 / x^2 is 1. So now that I have that done, I need to look at my tromial part of this to see if I can factor that. Again, always go ahead and write down the greatest common factor. And then go ahead and put your two boxes. Six. Well, I'm thinking that's going to be 2 * 3. And five is just going to be 1* 5. So let's put in 2x and 3x. we are subtracting our factors. So, let's see. I don't know. I'm just going to put five here and one here. So, let's see. We're going to get 2x - 15x. That's going to give me 13. Not what I need. So, let's try it again. Let's exchange places with my two and five. So, we'll put I'm not to my two and five. One, let's make that a one and five. So, now we have 10 x - 3x. So, that will give me seven, but I need a - 7. So, that means my larger number needs to be a negative. So, we're going to have 10 x and a positive 3x. So, that means my negative needs to go in front of my five and my positive needs to go in front of my one here. And this would be my answer. It is completely factored. Let's take a look at our second one. Well, I have a 16, 28, and a 30. So, I'm kind of thinking that my greatest common factor between those looks like a two. Now, I notice that they all have an x in common. So, I want to pull out an x. My lowest exponent is 1. So, we're going to have a 2x. That's going to leave me with 16 / 2 is 8. x cub / x is x^2. 28 / 2 is 14. x^2 / x is x. We're going to still have a y. 30 / 2 is 15. x / x is 1. And it's going to leave us with y^2. So we write down our 2x. Do our two parentheses, our boxes. Make sure that we get our y's as well of our as well as our x's in. Again, we are subtracting. Okay. So, when I look at my eight, I'm thinking 2 * 4 and 15 3 * 5. So, let's put those in. 2x and 4x and a three and five. It doesn't really matter where we start at. We just have to have some place to start. We're again subtracting. So, we've got 10 xy and minus a 12xy. Well, that's not going to give me 14. So, let's make some changes here. We want to exchange our three and five. So, let's put five here and three here. So, that's going to give us 6xy - 20x y. Does that give me 14? Oh, it does. Awesome. Okay. Now, I want a positive 14. So, that means my larger number needs to be positive. So I want a positive 20 and a -6. My -6 to get that I need to put a negative in front of my three. So that means I would have to have a positive in front of my five. So then my answer would be this. And we're done.