WEBVTT 00:00:05.000 --> 00:00:19.151 What are the possible directions for this problem? It could say simplify or 00:00:19.151 --> 00:00:20.240 multiply. 00:00:21.320 --> 00:00:26.120 Just multiply, which we need to use the distributive property. 00:00:31.780 --> 00:00:37.231 And of course we now need the distributive property of multiplication over the two 00:00:37.231 --> 00:00:37.620 additions. 00:00:37.620 --> 00:00:40.260 Okay, and there are no like terms. 00:00:41.140 --> 00:00:42.260 That would be it. 00:00:43.220 --> 00:00:44.600 You could be writing descending order. 00:00:48.240 --> 00:00:53.700 Okay, so today we're doing the opposite, or the reverse. 00:00:53.700 --> 00:01:03.400 First, we're going to start with this and we want to end with this. 00:01:06.220 --> 00:01:08.240 What's the reverse process called? 00:01:09.620 --> 00:01:10.960 It's called factoring. 00:01:10.960 --> 00:01:14.920 I'll start with the definition. There's actually two definitions of the word 00:01:14.920 --> 00:01:35.840 To factor means to write an expression as a product. 00:01:35.840 --> 00:01:40.840 Right, this is not a product, this is a sum. 00:01:42.460 --> 00:01:46.080 This polynomial, first off, what would this polynomial be called? 00:01:47.960 --> 00:01:49.740 A fourth degree trinomial. 00:01:49.740 --> 00:01:52.140 know if we're able to write it as a 00:01:53.200 --> 00:01:55.240 And we give you the number 24. 00:01:56.020 --> 00:01:57.480 And I said factor. 00:01:58.520 --> 00:01:59.720 What does factor mean? 00:02:03.280 --> 00:02:04.660 To write a product. 00:02:05.660 --> 00:02:07.640 So what are some possible answers here? 00:02:11.960 --> 00:02:13.440 1 times 24. 00:02:15.760 --> 00:02:17.100 2 times 12. 00:02:18.820 --> 00:02:21.480 3 times 8. 00:02:23.700 --> 00:02:26.360 4 times 6. 00:02:27.260 --> 00:02:29.040 6 times 4. 00:02:29.540 --> 00:02:30.720 Same sort of thing. 00:02:31.160 --> 00:02:32.620 Is that it? 00:02:35.520 --> 00:02:39.680 How about 2 times 2 times 6? 00:02:43.140 --> 00:02:47.180 How about 2 times 2 times 2 times 3? 00:02:54.220 --> 00:02:55.980 How about... 00:02:55.980 --> 00:02:56.880 What else do I got? 00:02:57.400 --> 00:03:02.380 2 times 3 times 4? 00:03:02.580 --> 00:03:03.480 Is that right? 00:03:07.700 --> 00:03:15.399 There's a lot of ways to write this as a product. These are often called factor 00:03:15.399 --> 00:03:16.149 pairs. 00:03:17.280 --> 00:03:25.468 Is there two numbers? Two different factors? These are often not. So, factor is kind 00:03:25.468 --> 00:03:26.560 of ambiguous. 00:03:27.860 --> 00:03:34.540 okay what it means to factor because there's lots of different possibilities okay 00:03:36.740 --> 00:03:55.360 This is called the prime factorization: 2 cubed times 3 squared. 00:04:03.840 --> 00:04:12.380 factored it into its prime factorization. The product of all its prime factors lead 00:04:12.380 --> 00:04:32.760 to the correct exponent. Okay. Why don't I put a number 1 in front? True. Well, what 00:04:32.760 --> 00:04:39.740 if it's one squared. Is that fine? No? Is it the same thing? What about one cube? 00:04:42.660 --> 00:04:49.580 They're all equal. But the reason we don't put a 1, because the number 1 is not 00:04:49.580 --> 00:04:56.380 prime, it's not a prime number. Why is the number 1 not a prime number? 00:05:05.760 --> 00:05:08.740 What is the definition of a prime number? 00:05:09.100 --> 00:05:10.000 Numbers prime yet? 00:05:16.220 --> 00:05:19.880 It's only divisible by one in itself? 00:05:21.000 --> 00:05:26.000 Or only be written as a product of one in itself? 00:05:26.300 --> 00:05:27.520 That's only half the definition. 00:05:28.960 --> 00:05:31.320 There's a second half of the definition. 00:05:32.820 --> 00:05:38.960 because the number one is only divisible by one in itself. The second half is a 00:05:39.780 --> 00:05:45.640 A number is prime if it is divisible only by one and itself. 00:05:45.640 --> 00:05:54.480 not a prime number. It's part of the definition. Okay so the reason one is not 00:05:54.480 --> 00:06:01.180 prime is because we define it not to be a prime number. It's in the definition. So 00:06:01.180 --> 00:06:11.960 why is one not prime? Because by definition. Okay. Which does make it, every 00:06:11.960 --> 00:06:19.180 number can be written uniquely as a factor of prime numbers to certain 00:06:19.180 --> 00:06:27.040 powers. Okay, that's an important thing in number theory. But so this is the only 00:06:27.040 --> 00:06:29.840 prime factorization of the number 24. 00:06:42.760 --> 00:06:44.540 To factor means to write as a product. 00:06:45.820 --> 00:06:48.200 Okay, so To factor means what? 00:06:50.880 --> 00:06:52.180 To write as a product. 00:06:53.660 --> 00:06:55.540 Okay, so what is a factor? 00:06:58.520 --> 00:07:15.782 Okay, one is a factor, 24 is a factor. In fact, what are the factors of 24? 1, 2, 3, 00:07:15.782 --> 00:07:20.960 4, 6, 8, 12, and 24. 00:07:24.560 --> 00:07:32.787 So what do all these numbers, these are all factors of 24. So what's it mean to be a 00:07:32.787 --> 00:07:33.537 factor? 00:07:37.660 --> 00:07:42.340 There's kind of two different definitions, but basically as far as numbers go, 00:07:42.340 --> 00:08:02.660 sorry this is the noun, a number is a factor of another number. 00:08:02.660 --> 00:08:09.080 divides evenly into it. 00:08:12.240 --> 00:08:15.080 We'll have to say if it divides evenly into it. 00:08:21.440 --> 00:08:35.928 Another definition is each, let me just call it a thing, in a product is called a 00:08:35.928 --> 00:08:36.780 factor. 00:08:46.440 --> 00:08:50.440 So these are a bunch of the, probably most are all the things. 00:08:50.940 --> 00:08:52.600 Each one of these things is a factor. 00:08:53.460 --> 00:08:55.580 A factor, a factor, a factor. 00:08:56.080 --> 00:09:00.340 Everything inside a product called a factor. 00:09:00.580 --> 00:09:03.300 Or if it divides evenly into it, it's a factor. 00:09:03.300 --> 00:09:31.140 Okay, once you find the prime factorization of 72 00:09:33.800 --> 00:09:37.920 I want each kind factor to the correct power. 00:09:37.920 --> 00:09:39.540 The prime factorization is 2 cubed times 3 squared. 00:09:41.340 --> 00:09:42.240 Is that right? 00:09:43.580 --> 00:09:45.420 These factor it, each of the prime factors. 00:09:45.420 --> 00:09:47.040 What are all the factors of 18x squared? 00:09:48.620 --> 00:09:49.680 Now that's the prime factor. 00:09:49.680 --> 00:10:06.151 What are all the factors of 18x squared? Now we got not just a number but 00:10:06.151 --> 00:10:07.180 polynomial. 00:10:07.180 --> 00:10:20.860 So we start with the numbers. There are factors of 18. Which are what? 1, 2, 3, 6, 00:10:20.860 --> 00:10:22.380 9, 18. 00:10:25.940 --> 00:10:37.160 Okay, is x a factor? Yeah, I could write this as 18x times x, it's a factor, or in 00:10:37.160 --> 00:10:47.100 other words 18x squared divided by x is 18x, it divides in it evenly. So x is a 00:10:47.100 --> 00:10:55.820 factor? Is x squared a factor? Yeah, right here we already got a product. 18 is a 00:10:55.820 --> 00:11:06.420 factor, x squared is a factor. What about x cubed? No. Okay, 18 x squared divided by 00:11:06.420 --> 00:11:11.960 x cubed is 18 over x, which does not divide any evenly. We end up with 00:11:11.960 --> 00:11:22.973 denominator. Okay so not x cubed. What other factors are there? Definitely 18x 00:11:22.973 --> 00:11:23.820 squared. 00:11:23.820 --> 00:11:51.040 is 2x a factor? Yeah 3x yeah 6x 9x 18x what about 2x squared yes 3x squared 6x 00:11:51.040 --> 00:12:01.280 squared, 9x squared, and 18x squared. Those are all the factors of 18x squared. 00:12:02.160 --> 00:12:16.940 Its prime factorization is 2 times 3 squared times x squared. 00:12:23.540 --> 00:12:31.565 Two times three squared times x squared. It's that simple. It's one of every prime 00:12:31.565 --> 00:12:32.100 factor. 00:12:32.100 --> 00:12:39.300 X is a prime factor to whatever power that's its prime factorization 00:12:51.100 --> 00:12:54.140 Find this prime factorization 00:12:54.140 --> 00:12:56.500 We get that. 00:12:58.340 --> 00:13:02.723 It's just the prime factorization of the coefficient times the rest of the 00:13:02.723 --> 00:13:03.473 variables. 00:13:09.060 --> 00:13:10.600 Slightly new topic. 00:13:13.500 --> 00:13:21.780 find the common sorry 00:13:37.480 --> 00:13:43.700 What are the common factors of 20 and 24? 00:13:43.700 --> 00:13:50.240 or let me list the factor to 20. 00:13:50.580 --> 00:13:54.340 One, two, five groups for. 00:14:14.620 --> 00:14:20.700 So, the common factors are... 00:14:36.040 --> 00:14:37.380 I forgot four here. 00:14:44.400 --> 00:15:04.440 The common factors are one, two, and four. The greatest common factor is four. 00:15:04.440 --> 00:15:08.700 largest of all the common factors. Okay. 00:15:13.700 --> 00:15:22.660 20 is 2 to the second times 5. 24 is 2 cubed times 3. 00:15:24.520 --> 00:15:26.700 Are those the two prime factorizations? 00:15:29.820 --> 00:15:33.720 Okay, and what acronym do we use for the greatest common factor? 00:15:35.220 --> 00:15:36.120 GCF. 00:15:36.920 --> 00:15:41.820 How can we use the prime factorizations to find the GCF? 00:15:41.820 --> 00:15:43.220 I 00:16:02.680 --> 00:16:09.520 How can we use the two prime factorizations to find the greatest common factor? 00:16:09.520 --> 00:16:12.260 Use every common prime factor to the lowest power. 00:16:20.900 --> 00:16:26.000 Use every common prime factor to the lowest power. 00:16:27.180 --> 00:16:30.160 Okay, and then how do I know? 00:16:30.620 --> 00:16:33.060 Is it 2 squared or 2 cubed or something else? 00:16:36.660 --> 00:16:41.360 Yeah, it's going to be the lowest of all the exponents. 00:16:41.360 --> 00:16:43.120 so it's going to be 2 squared. 00:16:46.760 --> 00:16:49.060 Okay, you could also think of this as 00:16:52.740 --> 00:16:57.820 2 times 3 to the 0 times 5 to the 1. 00:17:02.720 --> 00:17:07.942 Okay, so in fact it's one of every factor to the lowest power, so the two, between 00:17:07.942 --> 00:17:10.400 the two and the three is 2 squared. 00:17:11.660 --> 00:17:18.855 between 0 and 1 it's 0, which is just the number 1, and between 5 to the 1 and 5 to 00:17:18.855 --> 00:17:19.600 the 0, 00:17:19.600 --> 00:17:28.654 it's times 5 to the 0, which is just 2 squared. So it's one of every common prime 00:17:28.654 --> 00:17:29.660 factor to 00:17:30.480 --> 00:17:36.921 the lower of all the values, because 2 cubed does not divide evenly into this, but 2 00:17:36.921 --> 00:17:37.300 squared 00:17:37.300 --> 00:17:38.020 device in both. 00:17:38.020 --> 00:17:41.980 Now we've got some variables in there. 00:17:45.400 --> 00:17:48.580 So if we quickly find the prime factorization. 00:17:48.580 --> 00:17:51.520 It's the same thing but now we have variables in there as well. 00:17:52.100 --> 00:18:00.220 So between 2 cubed and 2 to the first, the smaller is 2 to the first. 00:18:00.860 --> 00:18:02.520 Between 3 squared and 3 squared. 00:18:03.700 --> 00:18:04.920 It's 3 squared. 00:18:07.440 --> 00:18:15.614 Between x cubed and x to the first we need a x to the first, y squared, y to the 00:18:15.614 --> 00:18:16.840 fourth, y squared, 00:18:17.900 --> 00:18:26.760 and there's no common Z so that'd be at 9 the 18 x y squared 00:18:52.340 --> 00:18:55.260 Okay, so what do we call this polynomial? 00:18:57.280 --> 00:18:58.860 Fourth degree trinomial. 00:18:59.300 --> 00:19:02.400 We're going to factor out the greatest common factor. 00:19:03.640 --> 00:19:08.220 So we look for the greatest common factor between three expressions or three 00:19:08.220 --> 00:19:09.120 monomials. 00:19:10.420 --> 00:19:13.160 We start the numbers 3, 12, and 18. 00:19:13.620 --> 00:19:16.546 We really don't even have to start factoring them. What's the largest number that 00:19:16.546 --> 00:19:17.800 goes into all three of them? 00:19:19.780 --> 00:19:22.560 Between x to the fourth, x cubed and x squared? 00:19:23.680 --> 00:19:25.500 x squared goes in all of them. 00:19:25.800 --> 00:19:29.060 That's the greatest common factor. You put parentheses. 00:19:33.040 --> 00:19:34.700 3x squared times what gives 3x to the fourth? x squared. 00:19:34.700 --> 00:19:38.540 gives you 3x to the fourth? x squared. 00:19:40.620 --> 00:19:44.360 3x squared times what gives you negative 12x cubed? 00:19:48.620 --> 00:19:51.500 3x squared times what gives you 18x squared? 00:19:51.920 --> 00:19:52.820 Six. 00:19:56.480 --> 00:19:57.480 And that's it. 00:19:59.680 --> 00:20:02.160 The result is 3x squared times the quantity x squared minus 4x plus 6. 00:20:02.440 --> 00:20:08.928 You find the greatest common factor between each of the terms, bring it on the 00:20:08.928 --> 00:20:09.360 outside, 00:20:09.360 --> 00:20:12.100 and then determine what we need to multiply to get that. 00:20:12.720 --> 00:20:15.820 In fact, that should be the results on our very first problem. 00:20:16.700 --> 00:20:17.900 Is that right there? 00:20:17.900 --> 00:20:19.420 Let's try another one. 00:21:10.360 --> 00:21:15.840 Between 4, 8, and 18, the numerical GCF is 2. 00:21:17.640 --> 00:21:23.780 Between x cubed, x squared and x to the 4th, the greatest common is x squared. 00:21:23.780 --> 00:21:27.060 y to the first, y to the fourth, y squared. 00:21:29.300 --> 00:21:31.760 y to the first 00:21:31.760 --> 00:21:33.680 is the smallest of the exponents. 00:21:38.280 --> 00:21:39.180 And then 00:21:39.660 --> 00:21:43.060 2x squared y times what gives us this? 00:21:46.700 --> 00:21:47.600 x 00:21:49.780 --> 00:21:52.380 2x squared y times what gives us this? 00:21:59.980 --> 00:22:02.880 2x squared y times what gives us this? 00:22:09.200 --> 00:22:13.160 We factored out the greatest common factor. 00:22:16.700 --> 00:22:21.725 I could factor out negative 2 instead, but that would not be the greatest common 00:22:21.725 --> 00:22:22.475 factor. 00:22:25.660 --> 00:22:28.400 But why is that not the greatest common factor? 00:22:28.400 --> 00:22:30.560 Because negative 2 is 00:22:31.420 --> 00:22:37.342 Less than positive. So we, when we're just factoring out the greatest common factor, 00:22:37.342 --> 00:22:39.880 we never factor out a negative. 00:22:40.160 --> 00:22:43.780 Sometimes we need to factor out a negative. That will be important when grouping. 00:22:44.420 --> 00:22:48.480 But for right now, the greatest is always a positive factor. 00:22:51.860 --> 00:22:53.300 And that's it. 00:22:53.300 --> 00:22:55.160 Okay, kind of a new topic. 00:23:13.940 --> 00:23:15.380 Okay, going back to multiplying where we 00:23:15.380 --> 00:23:22.051 We talked about this the last couple of days. What property do we use? The 00:23:22.051 --> 00:23:22.940 distributive property. 00:23:22.940 --> 00:23:29.180 properties. I'm gonna do it the long way, not our shortcut. I want you to write this 00:23:29.180 --> 00:23:34.500 out and you'll see why in a minute. I'm gonna first take this, distribute the 00:23:34.500 --> 00:23:57.300 whole thing, each of these. Then we use the distribute property again. Again. 00:23:57.300 --> 00:23:59.860 And then we typically write it in descending order. 00:24:23.140 --> 00:24:24.260 Okay, that's what we did the other day. 00:24:33.280 --> 00:24:35.140 Okay, next. 00:24:37.240 --> 00:24:41.820 I'm just going to say factor. 00:24:46.740 --> 00:24:48.560 We look at the four terms. 00:24:48.560 --> 00:24:55.140 What's the greatest common factor between those four terms? 00:24:57.140 --> 00:25:01.040 Yeah, one. So can we, we could factor out a one, we're not going to. 00:25:05.860 --> 00:25:08.020 What's it mean to factor? 00:25:10.560 --> 00:25:11.720 To factor means to write as a product. 00:25:11.720 --> 00:25:12.520 to write as a product. 00:25:12.520 --> 00:25:25.040 Besides multiplying by one, is it possible to write this polynomial as a product? 00:25:25.040 --> 00:25:38.780 We want to rewrite the four-term polynomial as a product of two binomials. 00:25:38.780 --> 00:25:48.480 We know it factors because we started with two binomials and multiplied them. 00:25:48.480 --> 00:26:08.760 started with it factored already. We multiplied it out. So how in the world 00:26:09.740 --> 00:26:11.620 The first group has a greatest common factor of 3x. 00:26:19.320 --> 00:26:20.960 The second group has a greatest common factor of negative 4. 00:26:22.300 --> 00:26:23.420 Negative four. 00:26:24.520 --> 00:26:31.100 and I factor it out. And then once I get it here, what do we have? We really only 00:26:31.100 --> 00:26:51.700 have one term, this plus this, but we have a common binomial factor. If we have 00:26:51.700 --> 00:26:54.640 for 3x minus 4. 00:26:57.480 --> 00:26:59.360 This is called factor by grouping. 00:27:11.340 --> 00:27:21.680 Can only be used when they're 00:27:21.680 --> 00:27:23.260 are four terms. 00:27:30.780 --> 00:27:35.000 Well, it could be six, but that gets complicated. 00:27:37.140 --> 00:27:40.862 It could be eight terms, but yeah, we're only we're only going to do it when there's 00:27:40.862 --> 00:27:41.612 four terms. 00:27:42.960 --> 00:27:46.820 The first step is always factor out the greatest common factor first. 00:27:47.860 --> 00:27:59.233 Side note, always factor the GCF first. But here the GCF is one, so we're not going 00:27:59.233 --> 00:28:01.240 to do that. 00:28:03.100 --> 00:28:12.220 Split the four terms into two groups: the first two terms plus the second two terms. 00:28:14.620 --> 00:28:19.200 And then within each group, we factor out the greatest common factor. 00:28:19.420 --> 00:28:26.840 So between 3x cubed and negative 4x squared, we factor an x squared out. 00:28:29.660 --> 00:28:31.280 3x minus 4. 00:28:34.260 --> 00:28:37.720 What's the greatest common factor between 6x and negative 8? 00:28:37.720 --> 00:28:39.500 2. 00:28:46.040 --> 00:28:50.000 Now we have two groups within each group. 00:28:50.220 --> 00:28:54.360 There's a binomial factor and 00:28:54.360 --> 00:28:59.280 it's a common binomial factor and so I 00:28:59.280 --> 00:29:00.360 factor that out. 00:29:12.020 --> 00:29:15.440 And when I factor it out of here, I'm left with the x squared. 00:29:16.920 --> 00:29:18.640 This plus is this plus. 00:29:19.860 --> 00:29:21.720 When I factor out of here, I'm left with the 2. 00:29:25.940 --> 00:29:32.580 So it's x squared plus 2 times 3x minus 4. 00:29:32.680 --> 00:29:33.400 And there it is. 00:29:33.400 --> 00:29:34.340 We factored that. 00:29:35.180 --> 00:29:42.973 a third degree or a cubic polynomial which has four terms into the product of two 00:29:42.973 --> 00:29:43.723 binomials. 00:29:47.140 --> 00:29:53.089 Okay, so we split up into two groups, factor out the GCF out of each group, and then 00:29:53.089 --> 00:29:53.420 check 00:29:53.420 --> 00:30:03.356 is there a common binomial factor, if so factor that out. Okay, why on this one are 00:30:03.356 --> 00:30:03.940 common 00:30:03.940 --> 00:30:09.560 binomial was 3x minus 4, but when we originally multiplied it, the common 00:30:09.560 --> 00:30:23.860 binomial was this. Why did that happen? It's because this polynomial with four 00:30:23.860 --> 00:30:31.680 terms was not written in descending order. If I took this and factor by 00:30:31.680 --> 00:30:36.320 grouping you will have a common x squared plus 2 with these two switched 00:30:37.580 --> 00:30:42.080 okay so but that was just side note let's try another one 00:30:42.080 --> 00:30:43.040 Actually, sorry. 00:30:43.220 --> 00:30:44.120 Let me change this. 00:31:00.680 --> 00:31:02.480 Now factor completely. First identify the GCF of all four terms. 00:31:09.240 --> 00:31:12.440 Okay, so the factor completely. 00:31:16.120 --> 00:31:18.040 The first thing we always do is what? 00:31:19.960 --> 00:31:22.620 Find the GCF and factor up the GCF. 00:31:22.760 --> 00:31:24.020 What is the GCF? 00:31:29.460 --> 00:31:30.380 Yeah, I think it's only 10. 00:31:31.920 --> 00:31:35.260 Factor out the common factor of 10. 00:31:49.180 --> 00:31:51.060 Now this has four terms. 00:31:51.200 --> 00:31:52.100 How are we going to do it? 00:31:53.920 --> 00:31:55.900 Factor by grouping. 00:31:55.900 --> 00:32:06.480 This 10 outside we just leave out here. Okay so I group into two groups this plus 00:32:06.480 --> 00:32:17.660 this. So between these two terms what's the greatest common factor? 3x squared. 00:32:28.380 --> 00:32:32.180 Between 12x and negative 16, what's the greatest common factor? 00:32:42.480 --> 00:32:47.340 And sure enough, we have a common binomial factor. 00:32:49.120 --> 00:32:53.920 Let's bring the factor that out. 00:33:06.060 --> 00:33:07.780 Let's put factor that out. 00:33:10.360 --> 00:33:31.720 and we're left with 3x squared plus 4. We usually put the coefficients of the 00:33:31.720 --> 00:33:35.820 monomial in front, but the order of the two binomials does not matter. 00:33:36.720 --> 00:33:37.620 That's fair. 00:34:16.400 --> 00:34:21.580 Find the GCF of the first group and the GCF of the second group. 00:34:33.500 --> 00:34:35.580 So the greatest common factor is? 00:34:36.980 --> 00:34:38.700 Two does not divide 15, so the four terms have no numerical GCF greater than one. 00:34:42.920 --> 00:34:45.020 So we don't factor out a one. 00:34:46.400 --> 00:34:47.360 We have four terms. 00:34:48.560 --> 00:34:51.180 Use factoring by grouping. 00:34:54.000 --> 00:34:55.800 First off, I can't write it like that. 00:34:56.140 --> 00:34:59.680 Why not? Because I changed that to multiplication. 00:35:02.700 --> 00:35:03.820 I can't 00:35:03.820 --> 00:35:06.620 do this. Why not? 00:35:08.820 --> 00:35:11.700 Okay, yet that negative 00:35:11.700 --> 00:35:15.360 is only with the 18. So, if there's a 00:35:15.360 --> 00:35:21.320 subtraction between the third term, we just have to put a little plus and then 00:35:21.320 --> 00:35:23.120 make sure we get the parentheses correct. 00:35:32.600 --> 00:35:35.760 And then we factor out the GCF out of here. 00:35:38.920 --> 00:35:40.740 Not just five. 00:35:42.960 --> 00:35:43.860 X squared. 00:36:04.860 --> 00:36:06.220 Factor out negative 6 so both groups contain the same binomial. 00:36:08.420 --> 00:36:09.320 It is very important. 00:36:10.600 --> 00:36:20.660 Factoring out positive 6 would produce the opposite binomial, so it would not match. 00:36:20.660 --> 00:36:39.240 Instead, factor out negative 6 so both groups contain 3x plus 8. 00:36:39.240 --> 00:36:49.640 Plus 8. Now we have a common binomial factor. 00:36:54.540 --> 00:37:02.305 Factoring by grouping works when four terms can be grouped to create a common 00:37:02.305 --> 00:37:02.860 binomial. 00:37:02.860 --> 00:37:07.004 because they have four terms doesn't mean it's going to work. Not all polynomials 00:37:07.004 --> 00:37:07.300 are 00:37:07.300 --> 00:37:14.497 able to be factored. Okay, but if it is able to factor, for example, if this were 00:37:14.497 --> 00:37:14.920 not, 00:37:14.920 --> 00:37:32.300 say this were 96 instead this would become well 16 and these would not be 00:37:32.300 --> 00:37:39.060 common so there'd be no way to factor that out so only sometimes it works it 00:37:39.060 --> 00:37:40.180 It has to work out nicely. 00:37:43.680 --> 00:37:47.220 Anyways, there are four. Let's do one more. If you get it right, 00:37:48.020 --> 00:37:48.960 we'll start homework. 00:37:48.960 --> 00:37:52.560 Try this final example. Start with the GCF. 00:37:52.560 --> 00:37:55.400 Factor out the GCF first. 00:37:55.400 --> 00:37:56.360 Check your result with a neighbor. 00:37:56.360 --> 00:37:57.460 We're seeing it got the same thing. 00:37:57.460 --> 00:38:03.922 On Thursday, we will learn to factor polynomials with three terms, called 00:38:03.922 --> 00:38:04.672 trinomials, 00:38:05.380 --> 00:38:09.920 and polynomials with two terms, called binomials.