### Greatest Common Factor & Factor by Grouping

- Factoring means to rewrite an expression as a product. Think of it as the opposite of multiply things together.
- The greatest common factor is the greatest quantity that would even divide into all of the terms. This could be made up of numbers and variables.
- If a polynomial has only one as its greatest common factor it is said to be prime.
- To factor by grouping
- Collect your terms into two groups
- Factor out the greatest common factor of each group
- Factor the entire polynomial, noting that they now have a common factor
- Rearrange and try again if they do not have a common factor

### Greatest Common Factor & Factor by Grouping

- 400 = 40 Ã—10
- 8 Ã—5 Ã—2 Ã—5
- 2 Ã—2 Ã—2 Ã—5 Ã—2 Ã—5

- 224 = 4 Ã—56
- 2 Ã—2 Ã—8 Ã—7

- 144 = 12 Ã—12
- 3 Ã—4 Ã—3 Ã—4
- 3 Ã—2 Ã—2 Ã—3 Ã—2 Ã—2

196a

^{4}b

^{3}c

- 4 Ã—49 Ã—a Ã—a Ã—a Ã—a Ã—b Ã—b Ã—b Ã—c

175g

^{2}hi

^{5}

- 25 Ã—7 Ã—g Ã—g Ã—h Ã—i Ã—i Ã—i Ã—i Ã—i

48u

^{2}v

^{3}w

- 4 Ã—12 Ã—u Ã—u Ã—v Ã—v Ã—v Ã—w
- 2 Ã—2 Ã—3 Ã—4 Ã—u Ã—u Ã—v Ã—v Ã—v Ã—w

- 24 = 2 Ã—2 Ã—2 Ã—3
- 60 = 5 Ã—12 = 2 Ã—2 Ã—3 Ã—5
- 72 = 6 Ã—12 = 2 Ã—3 Ã—2 Ã—2 Ã—3 = 2 Ã—2 Ã—2 Ã—3 Ã—3
- 24 = 2 Ã—60 = 5 Ã—12 = Ã—572 = 6 Ã—12 = 2 Ã—3 Ã—2 Ã—2 Ã—3 = 2 Ã—Ã—3

- 36 = 6 Ã—6 = 2 Ã—2 Ã—3 Ã—3
- 50 = 2 Ã—25 = 2 Ã—5 Ã—5
- 92 = 2 Ã—46 = 2 Ã—2 Ã—23
- 36 = 6 Ã—6 = Ã—2 Ã—3 Ã—350 = 2 Ã—25 = Ã—5 Ã—592 = 2 Ã—46 = Ã—2 Ã—23

12x

^{2}y

^{2},Â 18xy

^{3},Â 72x

^{3}y

- 12x
^{2}y^{2}= 2 Ã—2 Ã—3 Ã—x Ã—x Ã—y Ã—y - 18xy
^{3}= 2 Ã—9 = 2 Ã—3 Ã—3 Ã—x Ã—y Ã—y Ã—y - 72x
^{3}y = 6 Ã—12 = 2 Ã—3 Ã—2 Ã—2 Ã—3 = 2 Ã—2 Ã—2 Ã—3 Ã—3 Ã—x Ã—x Ã—x Ã—y - 12x
^{2}y^{2}= Ã—2 Ã—Ã—Ã—x Ã—Ã—y18xy^{3}= 2 Ã—9 = Ã—Ã—3 Ã—Ã—Ã—y Ã—y72x^{3}y = 6 Ã—12 = 2 Ã—3 Ã—2 Ã—2 Ã—3 = Ã—2 Ã—2 Ã—Ã—3 Ã—Ã—x Ã—x Ã— - 2 Ã—3 Ã—x Ã—y

16g

^{5}h

^{3}i,Â 36g

^{2}h

^{3}i

^{4},Â 48g

^{3}h

^{2}i

^{4}

- 16g
^{5}h^{3}i = 2 Ã—8 = 2 Ã—2 Ã—2 Ã—2 Ã—g Ã—g Ã—g Ã—g Ã—g Ã—h Ã—h Ã—h Ã—i - 36g
^{2}h^{3}i^{4}= 3 Ã—12 = 3 Ã—3 Ã—2 Ã—2 = g Ã—g Ã—h Ã—h Ã—h Ã—i Ã—i Ã—i Ã—i - 48g
^{3}h^{2}i^{4}= 4 Ã—12 = 2 Ã—2 Ã—2 Ã—2 Ã—3 Ã—g Ã—g Ã—g Ã—h Ã—h Ã—i Ã—i Ã—i Ã—i - 16g
^{5}h^{3}i = 2 Ã—8 = Ã—Ã—2 Ã—2 Ã—Ã—g Ã—g Ã—g Ã—Ã—h Ã—36g^{2}h^{3}i^{4}= 3 Ã—12 = 3 Ã—3 Ã—Ã— = Ã—Ã—h Ã—Ã—i Ã—i Ã—i48g^{3}h^{2}i^{4}= 4 Ã—12 = Ã—Ã—2 Ã—2 Ã—3 Ã—Ã—g Ã—Ã—Ã—i Ã—i Ã—i - 2 Ã—2 Ã—g Ã—g Ã—h Ã—h Ã—i

^{2}h

^{2}i

4x

^{2}y

^{3}z

^{4}âˆ’ 12x

^{2}y

^{2}z + 18xy

^{3}

- GCF = 2xy
^{2}

^{2}( 2xyz

^{4}âˆ’ 6xyz + 9y )

13a

^{3}b

^{4}c + 26a

^{2}bc

^{3}âˆ’ 39ab

^{3}c

^{5}

- GCF: 13abc

^{2}b

^{3}+ 2ac

^{2}âˆ’ 3b

^{2}c

^{4})

8r

^{7}s

^{5}t

^{4}âˆ’ 16r

^{6}s

^{3}t

^{2}âˆ’ 48r

^{8}s

^{6}t

^{4}

- GCF: 8r
^{6}s^{3}t^{2}

^{6}s

^{3}t

^{2}( rs

^{2}t

^{2}âˆ’ 2 âˆ’ 6r

^{2}s

^{3}t

^{2})

( 5x

^{2}âˆ’ 10xy + 4xy âˆ’ 8y

^{2})

- ( 5x
^{2}âˆ’ 10xy )

GCF: 5x - ( 4xy âˆ’ 8y
^{2})

GCF: 4y - 5x( x âˆ’ 2y ) + 4y( x âˆ’ 2y )

( 6x

^{2}+ 9xy âˆ’ 14xy âˆ’ 21y

^{2})

- ( 6x
^{2}+ 9xy )

GCF: 3x - ( âˆ’ 14xy âˆ’ 21y
^{2})

GCF: ( âˆ’ 7y ) - 3x( 2x + 3y ) + ( âˆ’ 7y )( 2x + 3y )

( 13s

^{2}âˆ’ 39st âˆ’ 25st + 75t

^{2})

- ( 13s
^{2}âˆ’ 39st )

GCF: 13s( s âˆ’ 3t ) - ( âˆ’ 25st + 75t
^{2})

GCF: 25t( âˆ’ s + 3t ) = 25t( s âˆ’ 3t ) - 13s( s âˆ’ 3t ) âˆ’ 25t( s âˆ’ 3t )

16x

^{3}âˆ’ 4x

^{2}âˆ’ 3 + 12x

- ( 16x
^{3}âˆ’ 4x^{2}) + ( âˆ’ 3 + 12x ) - 4x
^{2}( 4x âˆ’ 1 ) + 3( âˆ’ 1 + 4x ) - 4x
^{2}( 4x âˆ’ 1 ) + 3( 4x âˆ’ 1 )

^{2}+ 3 )( 4x âˆ’ 1 )

34y

^{4}âˆ’ 17y

^{2}âˆ’ 24y + 48y

^{3}

- ( 34y
^{4}âˆ’ 17y^{2}) + ( âˆ’ 24y + 48y^{3}) - 17y
^{2}( 2y^{2}âˆ’ 1 ) + 24y( âˆ’ 1 + 2y^{2}) - 17y
^{2}( 2y^{2}âˆ’ 1 ) + 24y( 2y^{2}âˆ’ 1 )

^{2}+ 24y )( 2y

^{2}âˆ’ 1 )

( 6m + 4 )( 5m âˆ’ 10 ) = 0

- 6m + 4 = 0
- 6m = 4
- m = [4/6] = [2/3]
- 5m âˆ’ 10 = 0
- 5m = 10
- m = 2

( 2a âˆ’ 14 )( 6a + 36 ) = 0

- 2a âˆ’ 14 = 0
- a = 7
- 6a + 36 = 0
- 6a = âˆ’ 36
- a = âˆ’ 6

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Greatest Common Factor & Factor by Grouping

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Objectives 0:09
- Greatest Common Factor 0:31
- Factoring
- Greatest Common Factor (GCF)
- GCF for Polynomials
- Factoring Polynomials
- Prime
- Example 1 9:14
- Factor by Grouping 14:30
- Steps to Factor by Grouping
- Example 2 17:43
- Example 3 19:20
- Example 4 20:41
- Example 5 22:29
- Example 6 26:11

### Algebra 1 Online Course

### Transcription: Greatest Common Factor & Factor by Grouping

*Welcome back to www.educator.com.*0000

*In this lesson we are going to take a look at the greatest common factor and the technique of factor by grouping.*0002

*First we will learn how to recognize a greatest common factor for a list of different terms*0012

*and how we can actually factor out that greatest common factor when you have something like a polynomial.*0017

*This will lead directly into the technique of factor by grouping, a good way of breaking down a large polynomial.*0023

*You are going to hear me use that word factor quite a bit in this entire section.*0032

*You are probably a little curious about what exactly factoring means.*0036

*Technically it means to write a quantity as a product.*0043

*We will be breaking down into pieces that are multiplied.*0047

*In a more practical sense, the way I like to think of factoring is that you are ripping things apart.*0051

*It is almost like doing the opposite of multiplication.*0056

*For example if I have 2 Ã— 3 I could put them together and get 6.*0059

*When I have the number 6 then I can factor it down into those individual pieces again 2 Ã— 3.*0066

*It is like multiplication but we are going in the reverse direction.*0072

*Now some expressions and numbers could have many different factors.*0077

*Let us take the number 12.*0082

*If you break that one down, you could look at it as 2Ã— 6 and you could continue in breaking down the 6 and 2 Ã— 3.*0085

*You have factors like 2 would go in there, 4 would go into 12, 3 would be a factor, 6 would be factor.*0095

*All those things could go into 12.*0103

*The greatest common factor will be the largest number that will divide into all the numbers present.*0110

*I will show you this to you twice just to get a better feel for it.*0116

*Suppose I'm looking at 50 and 75, the greatest common factor would be the largest number that could divide into both of those evenly.*0120

*5 could divide it into both of those evenly and that would be a pretty good choice, but is not the largest thing that could go in there.*0128

*The largest thing that could go in would be the number 25.*0136

*You will see that if I do take them both and divide them by 25, true enough they both go in there evenly.*0140

*25 is my greatest common factor.*0150

*We may only do this for pairs but you could do it with an entire list of numbers.*0155

*In this one I have 12, 18, 26, 32, and again we are looking for the largest thing that divides into all of that.*0162

*Sometimes a good way to find the largest thing that goes into all of them is just find something that works,*0169

*maybe something like 2 and end up reducing them bit by bit.*0177

*If I divide everything in here by 2 I would get 6, 9, 13 and 16.*0183

*Nothing else will go into all of those since 13 is a prime number.*0191

*My greatest common factor is 2 in this case.*0197

*It is not a very big number but it happens to be the largest in there that will go into all for these numbers evenly.*0201

*In algebra we are not interested in just single numbers we also want to see this process work out when we have lots of variables.*0209

*Let us see how this works out.*0216

*Maybe Iâ€™m looking at the numbers over the terms -16r ^{9}, -10r^{15}, 8r^{12}.*0218

*To find the greatest common factor, Iâ€™m first going to look at those numbers and see if there is a large number that could go into all of them.*0226

*I could divide all of them by 2, that would work but actually I think 2 is the largest one.*0234

*I will say that 2 will divide it into all of these evenly.*0242

*Divided by 2, divided by 2, divided by 2 and I would get -8, -5, 4.*0248

*We can also do this thinking about our variables.*0258

*What was the largest variable raise to the power that we can divide into all of them?*0261

*Think of using your quotient rule to help out.*0266

*With this one r ^{9} is the greatest thing that I can divide all of them by.*0272

*I would not have to deal with negative exponents or anything like that.*0279

*Let us write that over here, r ^{9}.*0284

*r ^{9} Ã· r^{9} would be a single r^{0} or 1.*0288

*r ^{15} Ã· r^{9} = r^{6} and r^{12} Ã· r^{9} = r^{3}.*0293

*Our greatest common factor would be 2r ^{9}.*0303

*Be careful when you are dealing with those variables and exponents.*0307

*Sometimes you will hear greatest common factor in your mind and you think you should go after the greatest exponent.*0310

*But as we can see in this example, it is not the case.*0315

*We actually took the smallest exponent because it was simply the greatest thing that could go into all of them.*0319

*Put that in mind and let us try this again.*0327

*In this one I have nothing but variables.*0330

*h ^{4} k^{6} h^{3} k^{6} and h^{9} k^{2}.*0332

*What is the largest power of h that could go into all of them?*0340

*It is going to be h ^{3}.*0345

*I picked up on that because I can see that looking in the middle one it is the smallest power.*0349

*Looking at all the kâ€™s, the largest exponent of k that could go into all them would be k ^{2}.*0354

*My greatest common factor will be h ^{3} k^{2}.*0364

*Let us see what this will end up reducing down to if I take that greatest common factor.*0373

*h ^{1} k^{4} h^{3} and h^{3} will cancel each other out.*0378

*k ^{4} I have h^{6} and I have no k that will end up cancelling each other out.*0388

*Being able to recognize the greatest common factor will help us in the next process.*0396

*Make sure it is pretty solid.*0400

*If you can recognize the greatest common factor you can often factor it out of a polynomial.*0405

*What I mean by factoring out is we are going to place it out front of a pair of parentheses*0413

*and put the reduced terms inside of that parentheses .*0418

*3m + 12 this is like looking at 3m and looking at 12, what is the greatest common factor of those two terms?*0423

*What could potentially go into both of them evenly and what is the largest thing that will do that?*0431

*The number 3 will go into 3m and the number 3 will also go into 12.*0438

*3 will be my greatest common factor.*0446

*Iâ€™m going to write that out front on the outside of the parenthesis.*0449

*What I write on the inside, what happens when I take 3m Ã· 3?*0453

*I will get just single m and when I take 12 Ã· 3 I will get 4.*0458

*Here I have taken a polynomial and essentially factored it into a 3 and into another polynomial m + 4.*0467

*The neat part about this is since factoring is like the opposite of multiplication you can check this by running through the distribution process.*0475

*If you take 3 and you put it back in here do you get the original answer?*0487

*You will see that in fact you do get 3m + 12.*0492

*That is how you know this has been factored correctly.*0496

*In some instances, just like with numbers when you are looking for the greatest common factor*0501

*it turns out you would not be able to find greatest common factor to pull from all of the terms or the largest thing will actually be 1 or itself.*0506

*In cases like that, we say that the polynomial is prime.*0513

*In other words it does not break down into any other pieces.*0517

*Let me give you a quick example of a prime polynomial 5x + 7.*0520

*There is not a number that goes into 5 and into 7 so I would consider that one prime.*0526

*How about 8x + 9y?*0534

*Individually those numbers are divisible, but there is not a number that goes in the 8 and 9 it would be a prime polynomial.*0542

*Let us work on factoring out the greatest common factor from various different polynomials,*0555

*just so we get lots of good practice with it.*0560

*Starting with the first one I have 6x ^{4} + 12x^{2}.*0562

*Let us hunt down those numbers first.*0567

*The largest number that would go into both 6 and 12 would be 6.*0570

*Let us look at those x.*0578

*What is the largest power of x that would divide into both of them?*0581

*That have to be x ^{2}.*0586

*We will write in the leftovers inside our parentheses 6x ^{4} Ã· 6x^{2}=x^{2} and 12x^{2} Ã· 6x^{2} = 2.*0592

*I factored out the greatest common factor for that polynomial.*0611

*Let us give this another shot with something has a bunch of terms to it.*0615

*30x ^{6} 25x^{5} 10x^{4}.*0619

*Looking at the numbers 30, 25, and 10, what is the largest thing that could go into all of them, 5 will do it.*0625

*Looking at our variables the largest variable that could go into all them would be x ^{4}.*0634

*It is time to write down what I left over 30 Ã· 5 = 6, x ^{6} Ã· x^{4} = x^{2}.*0645

*25x ^{5} Ã· 5 = 5, x^{5} Ã· x^{4} =x and 10x^{4} Ã·5x^{4} = 2.*0659

*That one has been factored out.*0675

*Continuing on, let us get into some of the trickier ones.*0678

*This one has 3 terms and has multiple variables in there.*0681

*It has e and t.*0685

*Let us look at our numbers.*0688

*What could go into 8, 12 and 16?*0689

*2 would definitely go into all of them.*0696

*4 is larger and it would also go into all of them and I think that is largest thing, so we will go with 4.*0698

*Let us take care of these variables, one at a time.*0707

*Looking at the eâ€™s, what is the largest power of e that could go into all of them?*0710

*This will be e ^{4}.*0715

*Onto the tâ€™s, the largest exponent of t that would go into all of them is t ^{2}.*0721

*Now that we have properly identified our greatest common factor, let us write down what is left over.*0732

*8 Ã· 4 =2, e ^{5} Ã· e^{4} =e and t^{2} Ã· t^{2} =1.*0737

*16 Ã· 4 = 4, e ^{6} Ã· e^{4} = e^{2} and t^{3} Ã· t^{2} =t.*0752

*Onto the last one, -12 Ã· 4 = -3, e ^{4} Ã· e^{4} = 1 and t^{7} Ã· t^{2} = t^{5}.*0766

*We have our factor polynomial.*0790

*One last one, I threw this one in so we can deal some fractions.*0794

*We will first think of what fraction could divide into Â¼ and into Â¾ ?*0800

*Â¼ is the only thing that will do it.*0808

*What could go into y ^{9} and y^{2}?*0812

*Look for the small exponent that usually helps out.*0817

*That will be our greatest common factor, let us write what is left over.*0823

*Â¼ Ã· Â¼ = 1 and y ^{9} Ã· y^{2} = y^{7}.*0828

*Â¾ Ã· Â¼ = 3 and y ^{2} Ã· y^{2} = 1.*0839

*At all of these instances you identify your greatest common factor first and simply write your leftovers inside the parentheses.*0849

*One quick thing that can help out, you can double check your work by simply multiplying your greatest common factor*0856

*back into those parentheses using your distribution property.*0861

*If it turns out to be the original problem, you will know that you have done it correctly.*0865

*In some terms, there is a much larger piece in common that you can go ahead and pull out.*0873

*Even though it is larger, feel free to still factor it as normal.*0880

*That is the hard part.*0884

*To demonstrate this I have 6 Ã— (p + q) â€“r (p + q).*0887

*It has that p + q piece again and both of its parts.*0894

*When I'm looking at the greatest common factor of this first piece and the second piece, it is that p + q.*0899

*Iâ€™m going to take out the p + q as an entire piece and that is my greatest common factor.*0910

*Inside the set of parentheses I will write what is left over.*0919

*From the first part there is a 6 that was multiplied by p + q so I will put that in there and there was a -r on the second piece.*0924

*This looks a little strange, I mean it seems weird that we can take out such a large piece, but unusually that it does work.*0933

*To convince you I will go ahead and multiply these things back together using foil.*0941

*What I have here is my first terms would be 6p, outside terms would be â€“pr.*0947

*Inside terms 6q and my last terms â€“qr.*0955

*Compare this after I use my distribution property on the original.*0962

*(6p + 6q) â€“ (rp + rq).*0970

*What you see is that it does match up with the original.*0984

*There is my 6p, I have my â€“ pr and â€“ rp, there are just in a slightly different order.*0988

*I have 6q and 6q -qr and I forgot to distribute my negative sign.*0995

*This should be a -rq and so it is the same term.*1007

*What you find is that you can pull out that large chunk of p + q and that leads to what is known as factor by grouping.*1013

*The idea behind factor by grouping is you try and take out the greatest common factor from a few terms at a time.*1024

*Rather than looking at all of them, just take them in parts.*1031

*This grades usually a very large piece and you can collect it into two groups.*1034

*Then you factor within those groups, you take out one of those large pieces.*1040

*This will allow you to factor the entire polynomial.*1045

*Sometimes factor by grouping does not seem to work or usually you end up struggling with a little bit.*1048

*If that is the case, try rearranging the terms and try to factor by grouping one more time.*1053

*It is a neat process and let us give it a try, when you factor by grouping on p Ã— q + 5q + 2p +10.*1060

*Watch how this works.*1071

*Rather than looking at all the terms at once, Iâ€™m going to take them two at a time.*1073

*A part of my motivation for doing that is if I were to look at all the terms all at once, they do not have anything in common.*1078

*Let us take these first two.*1086

*What would be the greatest common factor for p Ã— q + 5q.*1088

*q is in both of the terms so that is my greatest common factor for both of those.*1094

*What is left over? There is still a p in there and there is still 5.*1101

*Those are done.*1109

*Let us look at the next two terms.*1111

*What is the greatest common factor of just those two.*1115

*I can see a 2 goes into both of them and then let us see, the only thing left over would be a p + 5.*1119

*I will factor them into those little individual groups and now notice how I only have two things and they both have a p + 5 in common.*1131

* I'm going to take out the p + 5 as my greatest common factor of those two terms.*1142

*What will be left behind will be the q + 2.*1151

*This will represent my factor polynomials.*1156

*Let us try this again and see how it could work.*1162

*I have 2xy + 3y + 2x + 3.*1164

*Looking at the first two.*1170

*These have a y in common, let us go ahead and take that out.*1174

*2x will still be left when I divide 2xy by y and I still have a 3 over here when I divide 3y by y.*1187

*Looking at the next two terms, it looks like these ones do not have anything in common.*1198

*I might consider that the only thing that you do have in common is just a 1.*1205

*I could divide them both by 1.*1209

*I still have a 2x and I still have a 3.*1213

*Notice how we have that common chunk in there 2x + 3.*1218

*We will take that out 2x + 3 and then we will write what is left over just the y +1.*1223

*We can consider this one factored.*1237

*In this next example, be on the watch out for some negative signs which could show up as we factor out that greatest common factor.*1242

*Iâ€™m going to take this two at a time.*1251

*Looking at the first two, they do not have a number in common, but they both looks like can be divided by x ^{2}.*1255

*Let us take that out.*1262

*After taking our x ^{2} we would have left over a single x and a 3.*1268

*Let us look at the next two terms.*1280

*I can see that if I would go into -5 and 5 would divide into a -15 and they both have the negative sign.*1284

*That is important because Iâ€™m thinking ahead and try to think how I also have this common x + 3 piece.*1292

*Especially if Iâ€™m trying to factor by grouping.*1300

*The only way that is going to work out is if I take out a greatest common factor that is a -5.*1303

*What would that does to our left over pieces now?*1310

*-5x Ã· -5 = x and -15 Ã· -5 = 3.*1314

*I get those left over pieces like I need to, that same x +3 on the other side.*1324

*Now I have this I can take out my common piece of x + 3 and I can go ahead and write the leftovers x ^{2} â€“ 5.*1332

*Be on the watch out for certain situations where you need to rearrange things first.*1352

*In this one I have 6w ^{2} - 20x + 15w - 8wx.*1357

*And it is tempting to just go ahead and jump in there and try and factor.*1364

*Watch what happens if you do so.*1367

*First we take the first two and we would look for something common.*1370

*The only thing I can see that would be common is a 2 goes into 6 and into 20 and they do not have the same variables.*1375

*That is all I can do.*1385

*I have 3w ^{2} and -10x.*1386

*Looking at the other terms the only thing that I see common over there is they have a w in common.*1393

*What would be left over? I still have a 15 and have 8x.*1406

*That is definitely a problem because these pieces are not the same.*1413

*I need to do some rearrangement and retry this factor by grouping one more time.*1419

*Let us go ahead and rewrite this.*1433

*I will rewrite it as 6w ^{2} + 15w - 8wx and we will put that -20x on the very end.*1435

*Here is a little bit of my motivation for putting in that order.*1452

*When looking at the w's, notice how this one is a w ^{2} and this one is a single w.*1456

* I have the one is one more in power after the left.*1460

* And looking at the same w's, here is my w ^{1}, this is like w^{0}.*1464

*It is like I have lined things up according to the w power.*1470

*Watch how I factor by grouping works out much better.*1475

*Taking the first two they both have a w in common and I can pull that out.*1481

*It also looks like I can pullout 3.*1485

*3w will be like our greatest common factor.*1488

*What would be left over on the inside?*1494

*6w ^{2} Ã· 3w = 2w and 15w Ã· 3w = 5.*1499

*I have -8wx -20x, both of those are negative, I think I will go ahead and pull out a -4, that will go into both.*1510

*They both contain x so we will also take out an x.*1523

*-8wx Ã· -4x.*1532

*There are still 2w left in there.*1536

*-20x Ã· -4 = 5.*1540

*I can see there is that common piece that I wanted the first time.*1546

*We can go ahead and factor that out front.*1552

*2w + 5 and 3w - 4x and now this is completely factored.*1556

*Let us do one last one, and this is the one where we might have to do a little bit of rearranging just make sure it works out.*1575

*9xy â€“ 4 + 12x â€“ 3y.*1581

*What to do here?*1587

*Let us go ahead and put the things that have x together.*1590

*9xy + 12x - 3y - 4 and I have just rearranged it.*1606

*We will look at these first two terms here and take out their greatest common factor.*1612

*You can see that 3 goes into both of them and they both contain x.*1618

*It will take both of those out.*1624

*9x Ã· 3x, 9 Ã· 3 = 3, x Ã· x =1 and we still have a y sitting in there.*1628

*12 Ã· 3 = 4, x Ã· x = 1.*1639

*Those two would be gone.*1643

*That looks pretty nice and it is actually starting to match what I have over here.*1646

*Notice that the only difference is a negative.*1651

*I'm going to take out a -1 from both of the terms that not should be able to flip my signs and make it just fine.*1655

*-3y Ã· -1 = 3y and -4 Ã· -1 = 4.*1663

*I have that nice common piece that I need.*1672

*We will go ahead and factor that out .*1677

*3y + 4 and 3x - 1.*1681

*Now this is completely factored.*1690

*When using the technique of factor by grouping take it two at a time and factor those first.*1692

*Look for your common piece and factor that out and that should factor your entire polynomial completely.*1698

*Thank you for watching www.educator.com.*1705

3 answers

Last reply by: John Stedge

Thu Jun 22, 2017 10:54 AM

Post by Destiny Coleman on September 23, 2014

I did the work on Example 6 differently so I'm wondering if my answer works. Â First I rearranged differently. Â

Instead of changing to: 9xy+12x-3y-4 I used 9xy-3y+12x-4

This changed to -3y(-3x+1)-4(-3x+1)

The answer that I recieved was (-3x+1)(-3y-4)