Factoring out the GCF (Let's Learn Factoring)

all right let's get into it now in this case we're going to be this factoring process is going to be factoring out the GCF now in the first two examples I don't really have factoring out of GCF we just have some boxes with an area inside but again that's to reinforce what happened in the first couple of videos and if you're one of those students that said oh he's not teaching about factoring until this video let me just skip ahead this is not going to do it justice so please make sure you go back to those videos watch understand what I'm trying to have you understand before you get to a video like this because there something important that I want you to understand remember I talked about factoring is the process of rewriting an expression as a product when you think about the product as an area factoring is the process of rewriting what are going to be the sides that are going to make that area now the confusing thing about question number one and the reason why I wanted to do it is there's actually multiple correct answers right we could do 8 * 4 but that's not the only example so kind of going back to that original first video what I want you to understand and what's so critical for you to understand when you're doing factoring and something you're going to do in your head or write them down is to understand what are the numbers what are the factors that make up your number so 32 we could have 32 * 1 right we talked about that we could do a 16 * 2 we could do a 8 * A4 and I believe that is going to be all that we got right so there's three different factors so again any one of these would have worked I just chose an 8 * 4 but guess what if I wanted to rewrite 32 as the side lengths I could have done 32 * 1 16 * 2 or 8 * 4 right there's multiple correct answers and again you'll see what I'm talking about here when we get to the next video we're going to talk about the factors and how to factor trinomials but for right now I just want you to see that we need to understand the factors what makes up a number to understand what the side lengths possible side lengths could be now in this case I have a 4X as the area and if I was just going to rewrite this as a product there's really I don't have as multiple choices that I have here I can just re rewrite this as a 4 * X and that's really about all the options that I have right at least sticking with integers okay we're not going to get into fractions stuff like that we'll stick with integers those are going to be my options same thing over here we want to deal with integers no fractions right you with me hopefully you're with me now we're going to start getting into the interesting thing because this is the one that really I wanted to get into so we can understand these two problems because in reality I think we could all agree three four and five is really what you're going to be most likely seeing on test in quizzes and homeworks and for you to understand it's also what majority of the practice problems that you're going to be practicing in this course are as well as the quiz so let's focus on these but we need to understand what we and why we did stuff over here so 6X plus 6 what side lengths could I choose it's a very good question I don't know well sometimes we think about this and we say well I see a lot of sixes so what about if I made one side a six what would I need to multiply by to get a 6X plus a 6 well you might say well 6 * what is 6X you can say an x 6 * what is going to give me a six well that' be a positive one so therefore I could rewrite this box with an area of 6X + 6 to have the side length of 6 * a 6X + 1 now I know sometimes it gets confusing so remember last video we talked about the distributive property rewrite it right if I know that this times this gives me this area then let's write it 6 * x + one does when I multiply this using a distributive property do I get a 6X plus 6 yes I do okay so one thing that I want you to look at when you're trying to identify these side lengths is a lot of times I we talk about like factoring out or dividing out look at 6X + 6 what is the one number or term that they have in common they both don't share in X but they do share in six so when you bring out the six algebraically it's like you're dividing each term by six when I bring out the six what am I going to be left with a x + 1 that is going to be my other sidelength now for these next two videos I'm going to be a little bit more abstract I'm not going to do the box but if the Box helps you then rewrite it okay so now let's look at this next example kind of like Pretend This Is In The Box what do these two terms share what do they have in common what is what we call the greatest common factor between these two now when you look at this you can say well seven greatest common factor of seven well we have seven here and then this is seven divisible into 35 yes it is right seven divides into seven and seven divides into a 35 you know what I lied so I'm just going to bring this out so I can factor out a seven right I can divide a seven by both these terms 7 divide by seven is just going to be leave me with a one right and 35 7 is going to leave me with a five so that' be left over here so I'd have a one and over here it be a 5 now let's go and look at the terms what about variables what is the one variable that they have in common well you can see that X divides in x^ s and X divides an X so we can divide out an X to put on this side and what's going to be left over a x over here now notice that's multiplication and then over here the x is divide out so you're just going to be left with an X plus 5 so rather than using this box though I want to rewrite it like this when I divide out that term rather than putting on a side of a box your teacher might be like what are you doing you can put it on the outside of parenthesis so I divided both of these terms by a seven and an X and what was left over was an X plus a five so let's go and do it one more time we'll just not use the Box this time all right what does an 8x^2 and a four have in common obviously they don't have variables in common and a lot of times people see oh well eight like four divides an 8 yeah but they don't both have an eight in common we have to choose the largest number that is divisible into both of the numbers right eight does not evenly divide into four so the largest number that is both divided into that divides into both of them is going to be a four so rather than put it on ins side of a box I'm just going to put it on the outside of parentheses and what's less over when I factor out a four or when I divide out a four 8X Sid 4 is just going to be a 2 x^2 4 / 4 is going to be a positive 1 so hopefully you understand this idea of dividing out your common terms and then rewriting it like this because again ladies and gentlemen remember distributive property last video If you get confused if you double like double check yourself or question yourself like hm did I do it right factoring is just rewriting the expression as a product we can always go back and apply the operation of multiplication to double check our work 4 * 2x is an 8 x^2 4 * 1 is a positive4 ah okay I'm good that means it's time for me to get on to the next video