you know what I'd like to do right now I'd like to give you some examples of the types of problems we're going to be doing and then after I explain how to do we're going to do a few of these okay here's the type of polinomial I'm talking about type of u m expression that I want you to factor they look like this Stu like that I want you to notice something about this firstly um how many terms three terms does do these terms have the greatest common factor besides one no okay so the GCF thing it ain't going to work how many terms are there again three we'll Factor by grouping work no no cuz factoring by group grouping takes four terms so we have to have a new method and I'm going to teach you a new method on how to solve these so here's one and we're going to do all four of these examples at some point so we can have minuses up there we have different variables it's all the same idea as long as what you have here are three terms which share No greatest common factor now the way I always teach us I teach us according to what I call it the diamond method it's kind of like an x uh not really a diamond but I think it'll help you out really it's it's just a graphic organizer to help you organize your thoughts uh is what it is so one thing I want you to notice so how to factor how to one thing I want you to notice if you have three terms do you have understand that all the time with these three terms you could put them into this format where you have something X2 plus something X plus C and if you don't have any X cubes or higher then everything else that had more terms could be combined by either numbers or X's or X squares does that make sense to you okay so here's what we're going to do you know what maybe I better practices what that uh let's look at the first example right up here um what is the B the B here four no it doesn't go with any variables it's just the number he notice how it says BX so what's the B four good what's the C what's the a one one good there's a one there remember how the coefficient they're called coefficients and numbers in front of your variables the coefficients if there's not one there're still one because otherwise it' be zero and 0 times anything gives a zero so we have to have at least a one how about uh how about here what's our what's our a please one what is our keep in mind with our our coefficients also our a B's and C's it goes with a sign in front of it so a is one B is what good what's the C 15 how about here what's our a what's our B one very good what's our c a b c perfect are you guys okay with your ABCs next time won't you sing with me a no it's wrong I Micha Jackson so U here's how this works we're going to create what's called The Diamond method here how we set this thing up some teachers teach it differently I I like this way what we're going to do you know the letter B right that we we found in all these we're going to put B right up here we're going to put a * C right down here now the reason why I say a * C is because in about two one more section I'm going to show you when our A's are other did you notice this by the way every a was one up here yeah very special case Okay sometimes you're going have numbers out front and this technique changes a little teeny bit after this step but every single time you set this up the B goes here a * C goes down here I don't want you to forget that that's a * C because if the number is not one then that number is not just the last number some getting messed up on that now here's the whole deal this is not something I can teach you you need to be able to discover these numbers you're going to find two numbers these numbers must at the same time add to this one and multiply to this one at the same time add to the B and multiply to this product of a * C if you find those two numbers your factoring is done okay that's basically it for these for these cases so we're going to find two numbers let's just assume that uh that we've done that this would be your number one and this would be your number two you with me remember what factoring does does factoring destroy parentheses or create parentheses great okay in fact you're going to have wait how many numbers you have two so you have two factors you're going to need two sets of parentheses and here's how the factoring works for factoring three term pols once you found these two numbers once you found these two numbers we put X Plus number one and X Plus number two and that's fact can I say something here real quick and have you all listen to me so that I make sure that you know that I said it this right here jumping straight from here to here only works if your a is one if your a is not one you will have another step this is a shortcut it's a shortcut going from here here's a shortcut I can show you the long way if you want uh but it's a short maybe I will show you the long way one time but if your A's not one you can't do this n your have you heard me you might not understand it yet but just that you heard me there if a is not one you cannot do this if a is one easy very easy let me show you a couple of them right now in at least the last minute I'm going to do one of them that way you at least see it one so let's do uh let's do this one okay so here's the thought process going through I'm going to model it for you I'm not going to model for you but I'm going to model my thought process for you on how I would think about it first thing I check for a GCF do I have a GCF for those three terms no it's a three- term polinomial can I do factoring by grouping with every three- term polinomial if there's no GCF I want you to immediately think Diamond problem can you do that for me so three terms what's it called Diamond problem this the the Diamond method or Diamond Problem whatever this this is how you're going to factor it so we look for our a everybody what is our a one what is our B four C put the B here put a * C I want you always think a * C what's our a again times r c 1 * 3 is three now this is up to you you have to think of two numbers which add to this guy and multiply to this guy add to four and at the same time multiply to three I'm going to give you some hints here okay the signs of these numbers will help you if this number that you're multiplying to is positive these have to be the same sign both positive or both negative if that number's positive and that number's positive these will both be positive numbers if that number's positive and that number is negative these will both be negative numbers otherwise you'll have different signs and you got to figure that one out okay so right here I know that's positive same signs that's positive they're both positive numbers so I'm thinking about factors like 1 time three it's the only way that I'm going to multiply three and add to four 1 * 3 does not matter the order at all doesn't matter here's what I'm saying as soon as you have these two numbers and there's no a right here we can go directly to our factors and done I'm going to show you one time and only one time why this works are you ready for it please watch carefully because this can blow your mind uh I don't want you to cheat at it and not understand I want you to cheat at it knowing that this is actually mathematically possible okay so here's the idea do you do you really get that 1 plus + 3 gives you four and you get that the four is the middle number okay so here's what this allows you to do again you will have a shortcut here you don't have to do this every time what you would do is you say okay here's x s I'm going to use those two numbers to separate this + 1 x + 3x + 3 quick head not if you can verify that that's exactly the same thing if I combine my terms I would get that right now here's what's kind of nice how many terms do we start with three how many terms do we have now four what can we use with four terms grouping grouping this is why it works so nice if you group these two hey we just did that factor the X Out X+ one factor the three out oh huh X+ one you see it we just did it x + 1 x + 3 we know Factor group I'm not going to re explain it to you factor that out we get an X we get a plus three and those two numbers are exactly what those two numbers are and they will be all the time so do do you need to go through this every time no no you can jump directly to here okay so this for this type of problem I don't care about here's what I do care about please listen carefully here if this number is not one as soon as I put a two there you have to do it this way did you did you see the difference this right here jumping directly from here to here is a shortcut and it works every time as long as your a is what okay that's what I want you to know did today make sense for you we're going to jump right back on this tomorrow all right so let's continue we're going to keep up with this factoring of trinomials and probably for the rest of the day I'm going to sound like a broken record because I want to beat this into your heads so that you think the way that I think about these okay uh that way you get them right all the time so when we're factoring whenever whenever we're factoring basically anything first question that we have with pols uh where you have all the same variable is firstly is it in order I'm always going to ask you that so is this in order how we like to see our our polinomial basically descending exponents where the constant is at the very end is that in order for us you what I'm saying about in order there's X squ there's an X and then there's a constant at the very end that's what we like to see also is the first term positive we like to see that too so if we're going to factor we want to make sure our first term becomes positive somehow through Factor next thing we check for do we have a GCF a greatest common factor that we can pull out of these three terms okay after you check those things is it in order is the first term positive do we have a GCF after you check those then we start looking at the number of terms that we have if we have four terms we already determined that the four terms we use oh everybody should know it four terms we use that was like two people oh my gosh if you have four terms what how do you factor in this class that was better that was more than two people uh if you have three terms the only thing that we can do in this class the diamond method I call it the diamond method it's just factoring trinomials I call it Diamond method because it's a it's just a nice way to remember so the way we go through these well I showed you you're all familiar with your ABCs right what's the a here what's the B what's the C 15 anytime you have a three- term polinomial and you factored out the GCF you're going to go to the diamond problem you're going to make sure of course it's in order and uh no GCF and the first term is positive after you do that the B coefficient goes here the a * the C goes here and then you find two numbers the numbers must add to the B and multiply to the a * C so this is really up to you to be able to find these now I can give you some hints like I I told you I would so I'll do that for the first four examples and then really it's up to you uh I'll give you every case of these different things that you have but then it's it's kind of on you to find them so here that number's positive you're multiplying to that number meaning that both of these signs will be the same positive times a positive is a positive negative * negative is a positive these are going to be the same sign also you're adding to a negative if these are the same sign and they add to a negative they both have to be negative so right now I know that that's a negative that's a negative now that makes it easier that way we're we're kind of limiting what we have to do as far as while we don't have different signs here so we're thinking about some numbers that multiply to 15 add to eight they're probably in your head right now what are they yeah and since we know they're both negative by this process of elimination we got5 and3 quick head out if you're okay with that so far now here's the most important thing that I want you to get the a determines what you do next if your a is one like this whole section is okay your A's always going to be one in this section but I'm trying to prepare you not just section by section but factoring if your a is one you get do a shortcut you are done practically with this problem almost done I mean the rest of it's really easy if the a is one you're practically done even Rhymes nice right the a is one you're practically done uh if the a is not one you're going to have more work to do and I think I alluded to that last time when I did the extra work for you remember that last like minute of class I did that I proved it basically well the shortcut works if a is one we just go well factoring creates parenthesis I've got two numbers here so I keep the variable that's up here x and x that's through foil how we get our x s i put the two numbers that I just found negatives become minuses negatives become minuses and that right there is factored that's the factorization for a three- term polinomial you will typically if you're doing done method you always get these two excuse me these two sets of parentheses so if guys feel okay with that so far can you check your work yeah yeah just distribute it foil it it's going to be exactly the same let me go real quick try two more examples with you just so you we really thorough and then I'm going to give you something to do on your own so next one we're going to move a little bit quicker but I'm still going to ask the same exact question so first question first question is this is this an order for us is the first term positive that's what we like to see is there a GCF a greatest color Factor for those these terms how many terms do we have those are the questions I want you to ask every time okay because that's going to lead you what through what to do now if there's three terms can I use factoring by grouping doesn't make sense that's for how many terms four that's right so three terms we have a diamond problem or a diamond method so we're going to make our Diamond can you guys tell me what's your a uh the a is always just numbers always numbers so it's a number it's always a coefficient good so what's our B one very what's our c what goes here good our B1 goes here a * c yeah I know I know a is always going to be one for us right now but I want you to get in the habit of of doing a * C think about it a * C because a lot of people when I start doing things like this they'll still put -42 and they'll get the problem wrong because we always want to make sure that we're multiplying this number times this number and putting here so in our case we got -42 I want you to think don't say it out loud think about right now as I'm thinking about these what two numbers these will work with don't say it out loud I want everyone to be able to do this okay this is something I can't really teach you you just got to go through and be able to find two numbers which add to negative one at the same time multiply 42 there are hints if that number is a negative these signs are different one's a positive one's a negative so know one of those is negative if that's a negative it means that the bigger of those two factors that make 42 2 is the negative number so for us I'm thinking six and seven did you find six and seven so 6 and seven is going to work but you got to pick the right one to be negative since this is a negative number and we're adding to this the bigger out of those is going to be the negative the smaller of those is going to be the positive absolute value wise is what we're talking and double check it please don't get any further tell you double check it is -7 + 6 equal to1 good deal is -7 * 6 = 42 y does it make sense to get this and have it wrong and then continue right we want to make sure that we're right now I told you something just a minute ago is this one of the ones that I can do a shortcut on and go directly to my factors or do I have to go through more work what do you think shortcut shortcut okay why because that's it that's all you know a is one a is one then you're done I like that you can use it if you want to trademark I understand that but um I got stuck on why the in the diamond method why it was a negative one right there you get one what's the number here oh gotta it can't be zero yeah okay so factoring a three term polinomial is going to give us two factors now here's the deal what variable do we have here y y so don't put X's here's what X's yeah put X's don't automatically just change your variable to X all the time it's really common because people are so used to X but if we have y's you got to put y so we're going to have y what's the next thing we're going to put here s- 7 so A7 me means minus 7 do we just put a six like that does that make sense positive 6 changes to a plus 6 that's the idea now does it matter the order in which you had these no multiplication is communative so if you had put your posit 6 and7 not a problem it's still the same factorization am I making sense to you guys so far okay I think we have one more and then I'm going to give you probably four to do on your own four or five I want to make sure you guys can do this okay you probably know the questions I'm going to ask you but I told you I warned you ahead time I'm going to be a broken record here because when I give you examples on your own or on your test I want you to think like this I want you to think through okay first thing uh is this polinomial in order is it in order for us it's important to have this in order second thing is the first term positive that's good we we need that for our factorization if it's not positive we run into some problems here all right uh next thing is there a GCF in our terms no that goes into all of our terms okay so we think order first term positive GCF that's that's what we think next we count the number of terms how many terms have we got not four so groupings off the table we're going into oh what do we use for three terms perfect so we're going to do it okay everybody what goes here what goes here good we multiply 1 * -12 we get -12 and then you're going to think of some numbers now that sign's negative it means one of these is negative one of these is positive because we're multiplying to a negative number doesn't matter where you put that negative as long as you just have one negative and one positive that number is positive means we're adding and getting a positive number means out of these two numbers the bigger one absolute value wise is the positive one so we're thinking oh my gosh uh well three and four work but three and four gives you 12 won get that one so I've got to have two and six somehow but I'm going to say well uh since the number we're adding to is positive I can't do -6 because if I did -6 and two that would give me so use that this uh kind of process of elimination almost or at least some critical thinking to realize the smaller number is negative the bigger number is positive and then we double check it -2 + 6 four oh yeah it's four -2 * 6 practically done do we have to go further or can we do a shortcut here why can we do the shortcut so then we're going to do wait you say Z is one or a is one okay a is one Z I don't know what Z is we there's no way to solve this okay it's an expression not an equation so we can't solve it but the a the number in front of Z is one that's how we know we can go to the shortcut uh I proved it kind of proved it last time what do I put here and here [Music] Z you sound like my little math robots that's awesome what I here Z please feed me more numbers yeah okay next we go oh -2 - 2 POS 6 + 6 check it by foil your distribution and you're done I know it's going to work checked it before but you should check this especially when you have like a he like a hefty Duty problem and you're halfway in the middle of it and it asks you to factor you don't want to mess this up all right because this will this will make or break your problem so as long as we we can double check it make sure we're right then we continue show of hands if you feel like this is doable for you okay I want you to prove it to me I'm going to give you some examples I'll be walking around if you need this going to take some time so um take your time on it it's okay I'll give you maybe like 5 6 minutes to do these it should be about maybe a minute or two a problem when you're when you're doing once you get it down of course it takes practice to do that so let's start here for okay like I said I'm going to be walking around if you're struggling with with this idea not necessarily just one problem they can happen if you can't find the appropriate numbers they can happen you struggle with one problem I mean the idea if you're struggl with the idea let me know right now and I'll try to give you a hand also if you finish these quickly what should you be doing in the downtime between when I'm up there and around here what should you be doing check it make sure that you're right into the habit of that you guys start to see what I'm talking about about it's kind of up to you to find the numbers the setup's great but honestly it's just a it's just a graphic organizer it's really you thinking of these two numbers that makes this possible that's the big deal here and unfortunately I can give you some hints like the whole well one's negative one's positive deal but it really takes some trial and error sometimes to get these uh so it might take you some thought I can't just snap my fingers and make you you know make you really good at it it just takes practice and thought have you all done at least the first two of um okay I'll give you about another um another minute and a half or so try to wrap up as many as you can then I'm going to get start on the board can now all right tell you what I'm going to give you I'm going to get started up here either you're stuck or you probably finished at least three or four of them so we'll start on on this one that I I gave you first I hope that you were thinking through this the way I thought through it uh when I when I was modeling this for you so the first thing is it in order yeah I'm going to check that they're all in order it looks like they're all in order we want the square then the variable then just the the constant by itself I'm going to check to make sure that my first number my first term is positive positive positive so it's all set up for us I'm going to check to see if there's a GCF I'm going do this all at once that way I don't have to slow down while I'm going through each one okay no GCF that one doesn't have a GCF this one doesn't have a GCF that none of them have a GCF but we always check it first don't neglect that remember when I told you about GCF no matter what I tell you in the future always check for GCF you remember that go without saying anymore you always check for GCF no matter what when you're factoring after that we count the number of terms if they had four terms yeah be gring would be grouping here we have three terms in each case which means we're going to be doing a diamond problem every time and you'll get the hang of it really quick on what goes where the hard part about this is when you figure out that this is 9 1 * 20 gives me 20 the hard part isn't doing this okay this is the easy part I didn't give you the hard part I didn't I didn't really teach you how to do that every single time for every problem because I can't all these numbers are be different every time all right it's up to you to figure out well nine goes there 1 * 20 20 goes here now I got to add to that number and multiply to this number I know because I've been doing this a while right I'm pretty good at it you guys need some practice at this for some of you some of you guys are really good at it this going be five and four they're both positive they add to nine they multiply to 20 did you guys get that one okay after you do that don't just stop at a d problem this is just an organizer for you it doesn't solve it well I can't say solve it it does not Factor it for you what factoring means is you take this numbers and you use it you say well factoring means create parentheses factored means that I'm going to take these two numbers and if they're positive I put plus if they're negative I put minus and because I have a one here it means I can go to the shortcut I can do just my two factors and I know it's going to be right show F if you got at least that one if you got that one that means that you understand the idea of factoring if you didn't get the rest of them that means that you're you're struggling with finding the numbers that work there and that's okay you can work on that as long as you get the idea of factoring what I really want right now is that you understand the concept of in order do you the concept that the first term really it should be positive if you want to factor using these methods because it's really hard it's not you get that you get that the first thing you should be doing all the time with factoring is looking for GCF yes no do you get that with three terms Diamond problem is the way to go okay and lastly if we have an A that's equal to one after we do this we can go directly to our factors and if we don't have an A that's one we have more work that we need to do so fans if you understand all those Concepts then you get the factory now sometimes it might be a little difficult to find the numbers but that that's the idea so I think you you you've mastered the idea now it's just kind of working with it what number goes here five how about on the bottom what goes there that means different signs that's a negative different signs bigger one's positive so I'm looking at 9 and four is it negative 9 or positive 9 and4 that adds to five that multiplies to 36 so since we have one here all right that's awesome I can do x - 4 I can do x + 9 I use those two numbers that4 - 4 POS 9+ 9 and I know that I could check that with foil and it's going to be absolutely right you guys two for two good all right next one still the same thing we've checked the conditions for our Diamond problem already uh what number is going to go up top3 on the bottom please now that's a positive yeah m and that's a negative means they both have the same sign and that's a negative they're both negatives they have to both be negatives now the numbers that multiply to 22 there's not many of them all there's 1 and 22 and there's 2 and 11 so it's got to be 2 and 11 so 2 and 11 well that's pretty easy since they're both the same sign does that add to -3 y good to go there's a one here means I go directly to my factors and now we factored it factoring always creates parentheses you have those two numbers you're going to create two parentheses so far so good okay next up conditions are met for our Diamond problem we're all good no GCF all that fun stuff -3 -40 we go okay well uh if that's a negative these things have to have different signs don't they a negative posi yeah it's got to be negative and a positive now that number is a negative meaning whatever we find here whatever factors work the bigger one absolute value wise it's going to be negative the smaller one's going to be positive I'm looking at what eight and five somehow now because that's negative it's got to be8 and POS 5 let's double check though see adding them3 yeah that works multiplying them4 that works too now just put them in your in your factorizations why don't we have to do the extra work on this why can we go directly to my factors why can we do the shortcut explain it one more time very good by the way what variable should I use here got to make sure you do that can you double check your work you should so if V feel okay with these ones so far okay last one GCF no in order how well uh three terms means denal problem number here is six number here is give me two numbers that add to six and multiply to 15 dare you I dare you to can you find did you try it at least okay how long did you spend trying it a long time right I up okay this proves to you something that I I wanted you to try I'm not going to just give you stuff for free a lot of the time I have you work for it um do you believe me when I say there's no two numbers that work here okay then you should also believe me when I say that not every three term polinomial is factorable you're going to run across some that this does not work and this this does not work and this doesn't work and this doesn't work this is one of those times you go um I don't know and then you go and you go what am I supposed to do with this and you go well nothing you can't Factor this there's no two numbers that allow you to factor it and so what you call it you don't you don't do any other work uh you don't make something up it's not factorable we call that situation Prime it's a prime trinomial it just means you can't Factor it you need to understand that there's some trinomials some pols that you cannot Factor so Fant if you understand that hopefully that proved it to you after you struggled with finding those numbers and man am I am I a little slow today or did Leonard make me darn you Leonard you got me well sometimes you can't do it can I move on a little bit do you understand the idea of factoring when your a is one I'm going to move on a little bit and give you some special cases of things that you can do they look a little weird but stick with me here it's the same basic idea so some special case pols that that I want you to see so first one okay that looks a little funky because it's like nothing that we've really seen before uh besides some of those four terms but uh when we look at it closely how many terms do we have three terms that means grouping is not going to work all right also is it in order well yeah kind of I we have X squ then we have X Y then we have y^2 that's kind of nice uh but the order thing doesn't doesn't really flow because we have two different variables all right so all right that looks looks fine uh let me tell you something if you have three terms on certain special cases you can still make them a diamond problem sometimes you can't this is one of the special cases where you can I'm going to show you that one time so if we did the diamond problem here because we have three terms also check this out do we have a GCF I don't want to forget that ever do I have a GCF no besides a one so what number would go up here if you had to put one good and here same signs both of them negative this one should be kind of easy 10 yeah if you do -1 do you understand why they have to be both negatives in this case got to add to a negative got multiply to a positive it's the only way it's going to work this adds to -3 yeah this multiplies a POS 30 so check it out if you didn't have listen if you didn't have the Y's if these weren't here what you would have you see what I'm talking about if you didn't have the Y's you'd Factor this and it would be XX and you do - 10 and you do Min -3 would you agree with that yes to get the Y's just put a y that's going to work if you notice that this will give you the X2 won't it and this will give you the -3 X Y this will give you -10 X Y 13 y this will give you POS 30 y^2 one more thing before I answer your question um if you do this by that there's remember that method I showed you like the last minute class last time it's earlier on the on the video if you're watching you can still do it by separating this if you didn't - 10 x y - 3x y do you remember me showing that to you if you don't maybe go go back and refresh remember on the video this has how many terms four and do you remember thanks one of you uh do you remember that these terms add to that number that means that I can split this up into two extra terms I could do my Min - 10x y - 3x y does this still make -3x y okay and then my plus 30 y^2 grouping still works this is a longer way remember I told you if that's a one you can shortcut it do are you with me if it's a one you can shortcut it if it's not a one you have to do this but I'm just kind of proving to you that this will still work um either way so if you factor out the X we get x - 10 y oh look at that if we factor out the three oh oh do you remember what this does come on tell me if I have a minus there what's that force me to factor out a negative so I factor out my -3 I get oh okay oh I missed something what else that's right so here I have a y I have a y^2 so I'm factoring out My3 it's forcing me to factor negative this says three this says y so if I factor out out -3 y I get X what's that sign going to change to if I factor out a negative and I'm going to get 10 y do you see that it's going to work now I've covered this enough times for you hopefully that you see this is going to be obvious there's two big terms these are the same factor if I continue to factor I get x - 10 y we get x - 3 Y and I hope I'm I'm really hoping that's exactly what I showed you the first time did I show you that mhm okay so it still works if that's a one you can still do the shortcut just don't neglect the wise just a little addition there show fans have explained that well enough for you these don't happen all the time but if I don't show it to you people are going to go oh my gosh cuz it looks a little weird doesn't it what in the world's going on same idea same idea okay let's keep on moving here um oh this is a good one [Applause] now you look at you go wait a minute that's weird what's weird about this we never seen those before right and besides maybe um factoring out the the GCF but does this have a GCF hello have a GCF is it in order yes mhm in order 42 constant got it uh no GCF is the first term positive yes we like that how many terms do we have three what do we do with three terms let's try the DI so if we try the diamond we're going to have 10 we're going to have 21 can you verify that for me 10 and 21 okay can you think of two numbers that add a 10 this oh this is easy one this is a good one I love these ones they're all positive what is it 3 and seven yeah 3 and seven now you can do this a couple ways you can do the shortcut on this as long as you understand what the variable uh believe you can still even group it I'll I'll show you that if you really want so here's X to 4th do you remember that these split that term up if you get this the next section is going to be so freaking easy for you like good stuff okay so if you understand what I'm about to do that these numbers had to add to that one therefore these numbers are how I split this term up + 3^2 + 7 X2 are you with me still yes and then plus 21 tack that onto the back end look it look it the only reason why we're doing this only reason why we're doing this right now is to change three terms into four terms why do I want to change three terms into four terms why and grouping's easy that's why so once I do this I can group and here I'm I'm just going to do it for you because we've covered it so many times okay here the greatest common factor is X2 I do it I get x^2 + 3 plus here's the other one I factor out a seven I get x2 + 3 is that going to help us yes no what do you think yeah because there's two big terms now and we have the same factor if I factor out the x^2 + 3 as we've done many times before I remove this by factoring by division remember factoring always creates another set of parentheses I remove this I get x2 I remove this by factoring by division I get plus 7 and that's completely factored for you isn't that kind of nice kind of weird right uh check it out could you have gone directly from here to here yeah yeah 3 three 7 s the only thing you got to realize is that that's not X2 anymore it's x to the 4th what do you need to get X to 4th you need an X2 * X2 and that's how you'd figure that one out show hands if that one made sense to you cool okay I know I'm not giving you a whole lot of U opportunities to do this on your own frankly we don't have a whole lot of time for that uh I I'm just kind of saying if you get this these are the same ideas I'm just giving you special cases that way when you see them on your test or in your homework you don't get super intimidated okay okay I can do this it's the same idea if you don't understand how to get directly from here to your factors please please trust me that you can always split these up and use grouping you can do that every time so if you're like man how in the world's get just use grouping how in the world you get from here to here just use grouping and it'll show up for you so if you ever get stuck what are you going to do grouping make four terms and group it and that's why you use these two numbers understood these ones it's pretty easy it's just a shortcut so the the real work the real stuff that we do all the time this is just a shortcut it's really this it's separated into four terms it's grouping them and it's finishing off factoring by grouping it's separating into four terms it's grouping them and it's finishing off your factoring by grouping you with me okay let me show you uh tell you we'll do two more and then we'll put all of this stuff together and deal with the case where a is not one is this stuff getting easier for you than when we started I hope so I hope it's not getting harder I me I hope that you're you're learning something here tell me something about this problem it's one of the first things we check GCF okay we checked ECF but first we probably want to check this order the order is this an order put it in order cuz if you start trying to do a diamond problem right now it gets a little funky uh especially because especially if you're a person that would put a is 30 don't do that uh put this in order first and then start checking the stuff so as soon as we arrange it that really helps us what's supposed to go first and then what1 remember that terms always go with the sign in front of them so we have the z^2 cool we get Theus 31 z um when you have a positive 30 I know there's not a sign in front of that but don't just put 30 I have z^2 - 31 z30 that looks really weird okay you need still a three term polinomial so you're going to put the Plus in there signifying that you're adding the 30 or that it's positive 30 does that make sense to you now what are we going to do what should you check for before Diamond problem does this have one no but we check and now we go okay three terms Diamond great so once we set up our Diamond problem now it's kind of a non issue I just want to make sure that you understand if it's out of order put it in order makes your life easier -31 we got wait a minute that doesn't work tell you what let's use our our method here they're both negative do you see why yeah got to make it positive by multiplying and negative by adding they both have to be negative only way this works if you have 30 and 1 so there it's -3 And1 does that add to- 31 does it multiply to positive 30 yeah so sometimes you might have to think on it don't give up on it like this one okay this was a one but some of them you mean don't don't give up right away and you still got to think about it um do I now here's a good question do I have to go through all this process and do the grouping no if I get stuck can I go through this process and do the grouping yes yes but with z the coefficient of z s being 1 I can do Z - 30 I can do Z - 1 and sure enough we are done could you check your work should you check your work yes am I going to cuz I'm lazy but you should because it's your test I've already passed this class like a long time ago at least last year I mean all right one more one more oops ni up actually do you want to try one you just try one on your own see if you can handle it m I think you can it's a little challenging not too bad a little challenging you just got to follow the steps that I've I've talked about got follow the steps I've talked about go for it see if you can do it is that [Music] what's the first thing that you checked for when dealing with this uh polinomial what's what did you check for order even before the GCF actually order is it in order that's great is the first term positive reason why we asked that because if it's not positive even if you did not have a GCF what you do here you'd factor out a negative okay that that's how the diamond problem works so the ne -1 would have been your GCF does that make sense to you so for inst if I did like like this first thing I'm doing here is factoring out the negative it's just changing all my signs and then I start going through that so here Order yeah very good first ter positive cool that's going to help me with my GCF now I check for GCF uh what what is our GCF here yeah you're GNA pick as much as possible so five for sure and then as far as variables remember going to lunch you got to go to a restaurant every can afford so x to the 3r is the biggest power that's shared by all of them so we're going to factor out the five and the X to the 3r and if we do I'm going to do it kind of quickly we're going to create brackets here we're going to have x^2 5 5 is 1 x 5 x3r is X2 minus cuz we're not changing signs we didn't factor a negative 25 5 is 5 x 4 of X the 3 is X another minus 30 / 5 is 6 x 3r x 3r is 6 * 1 is 6 which is how we get down that floor now a lot of rookies will stop right there because they go oh I factored you did is factoring a oneandone type of idea you can Factor many many times sometimes like three four times in a problem potentially it's ugly all right but you can do it so here we don't stop we check this now now we have a technique for solving these how many terms do do we have three you don't have to check the order cuz it's already in order you don't have to check a GCF because you already factored the GCF now you just do a diamond problem so if we do a diamond problem typically if you factor GCF these are pretty easy okay they'll they'll get really nice if you fail to factor the GCF these diamond problems can be really tricky because if you don't Factor the five out even if you do the X's 25 on the top and 150 the bottom that's that's pretty big right it's going to take you a lot of thought and then once you do that you'll still have a GCF within those factors which is going to be stinky so do your GCF first it'll save you a lot of time later anyway we're going to put our neg5 we'll put our -6 we go all right well uh they have to have different signs the bigger one's going to be negative what is it that's right6 and one please don't get confused on threes and twos all the time sometimes they're threes and twos but you got to make them work okay so this does that add to5 y does it multiply 6 okay so we're going to have if we just ignore this for a second if we had just this it would be x - 6 explain to me why I'm going directly here and I'm not doing this stuff please no Co a perfect yeah so we have x - 6 we have x + 1 now we're going to wrap this up with a bracket we're going to not forget about this guy 5 x 3r and that's completely factored I want to show hands that one makes sense to you you feel okay with it question um when you're on math Excel and you're turning your problems you have to have the brackets you know I don't think so I don't think that you do because that it's kind of redundant in this case uh the reason why we have the brackets here you do have to have them here okay uh down here because you're multiplying and multiplication is commutative and associative you really don't need them so you don't have to multiply these first and then do that you could have just like that be appro takes the double brackets on I'm sure it will'll using the double brackets I didn't know you can move yeah yeah yeah you can that's perfectly appropriate answer as well so if I was to put this as an answer on a test it would still be correct oh yeah yeah that that's usually the way that that I would put them the brackets just kind of hold it it's but as soon as you have it factored you don't need those those people graits good question any other questions okay because um this flows so nicely we're going to start the next section right going to skip 6.3 because it's a it's a way of teaching factor I really don't agree that much with I like this next method a lot better so we're going to skip to 6. 6.4 and we're going to put this idea right here to the test when a is not one so here's going to be my point if you understand this concept of splitting up your middle term this next section is going to be really easy do you understand this concept okay I taught it a certain way that way this would all make sense to you okay I had a method to my Badness so