 This video is part 2 of factoring. In this case, we're going to be looking for a is greater than 1 2x squared plus 11x plus 5 keep these two things the same and that's my a times my c Okay, so a c here is going to be equal to positive 10 this time and if we look at the b it's still 11 But when we make that x over here We have 10 up here and 11. It's a positive So I have the same signs my middle term is a positive So I have two positive numbers. I'm going to add together to get to 11 and that would be the 10 times the 1 So we have m as 10 and is one it really doesn't matter You could have said m is one and n is 10 just as long as you get them both listed So here's the ac method we take our 2x squared and keep it but remember we're going to Rewrite 11x with these two factors because it's just another way of writing the 11x It just takes two terms to do it. So we will say plus 10x and Then plus 1x so we take that m and n and we multiply it by x to get our middle terms And then we add the last term back on at the end So if you remember with four terms, we need to take the first two terms in the last two terms And when we factor here, we would have a common factor of 2x because they both have an x in them And then that leaves us with 2x. I need one more factor of x and Then 2 times positive 5 will give me 10x and the x is already on the outside so I don't need anymore and Here one and x and five don't really have anything in common, but they at least have a positive one in common if nothing else they're going to have that in common and Then one times x will give me that one x and one times five Positive five will give us that five at the end But remember with four terms it takes two times of finding the greatest common factor So we do it again, and we find out that the greatest common factor is that x plus five I'm not really scratching that out. I'm just thinking what's left over if I have that one already I'm left with 2x if I have the x plus five. I still have the plus one So this would be my factorization again. I did not cancel those out. I was just thinking Okay, the purple is just my thinking process So let's try this one Greatest common factor three negative 13 12. Nope. There is none AC that's the three times the 12 So AC is going to be 36 B That's my middle term and take the sign with this so negative 13 and now I'm ready to make my x and In the top goes my 36 and In the bottom goes my negative 13 you may be looking at this and saying I don't know what all the factors of 36 are I haven't really thought about all those. I want to show you a trick at this point So you're trying to find factors of 36 that might add up to negative 13, but you can't think about what the factors are of 36 There's a little trick that you can use in your calculator and what we're going to put in here in our calculator is AC divided by x And that's what we're going to put in our calculator over here And you literally could put in parentheses just like I did. What is my a it's three times my C which is 12 and Then divided by x or you could have put in I'll show you it doesn't matter If you knew that that's 36 like we do you could divide 36 by x we should get the same things So you put that in there, and then we're going to look at our table x and y Because because we divided by x now the x column is my It's one factor and the y column is my other factor and this y2 just shows you since these are the same things Then it shows you it didn't matter which form we put our equation in but I'm going to concentrate on these two And if I think about one and 36 I Need the negative numbers so if I go in here and look at negative 3 and negative 12 that's going to be negative 15 Negative 4 and negative 9. Oh, there's my negative 13 right there So I can come over here and say that this is negative 4 and negative 9. That's my m and n So let's see what we can do here. Remember with the AC method we put our first term and Our last term and then we leave space for the other two terms And our other two terms come from the m and n and all we have to remember to do is put an x with them And then drag them over here So we have them. Let me change my color minus 4x and minus 9x It doesn't matter which one went where it'll all end up factoring the same no matter what and those aren't x's those are t's Gotta keep consistent with our variables here So we take these two terms and the common factor would be t So I need a 3 and one more factor of t and I need a negative 4 And that would give me my 3t squared minus 4t and now when I have negative 9t plus 12 in here You got to be careful when you got this negative in the middle as your third term like that Typically not always, but typically it'll be a negative that you want to factor out And if you think about it, I need to get it to be a 3t minus 4 and right now my 12 is a positive So I probably do want that negative to come out of there So a negative and 9 and 12 have 3 in common That will leave me with negative 3 times 3 is 9 times t So 3t and negative 3 times negative 4 will give me the 12 And now I can see that these two things are the same So when I do my factoring of my first two terms in my last two terms That's my greatest common factor And my other factor would be the t on the outside and the negative 3 on the outside that make up my second factor Our final problem here. We have to look for greatest common factor Always remember that's the first thing you have to do. So 8 and negative 12 and negative 80 all have a common factor of 4 So our greatest common factor is going to be 4 And if I then find the other factor that would be 2y squared times 4 would be 8 y squared and if I multiply by negative 3, I'll have and Y I'll have negative 12 y and If I take 4 times negative 20, that'll give me negative 80 So when I think about my AC, I'm going to take the 2 times the negative 20, which is negative 40 And my B is going to be my negative 3 And so I come over to my calculator and I've already put in the negative 40 So we're ready to go look at the table and I'm trying to add up to negative 3 Well one and this would be 39 2 and negative 20 would be 18 negative 18 4 negative 10 would be negative 6 5 and negative 8 would be negative 3 So there they are we have a negative 8 and a positive 5 If you can and the reason why I wrote negative 8 first is because it makes it nice For that third term if you could write your negative first all the time now we have to take this polynomial and Find our solution from the rest of the factors from that So we still have our four, but we've got to find our two binomials and we're going to work on this polynomial So we have 2 y squared and negative 20 that we're going to put in here And then we're going to add the middle to be that minus 8 and Y and positive 5 y And your x Remember we were down here negative 40 and we had a negative 3 and we always put your negative to the left If you have opposite signs especially put your negative to the left that will make your third term a positive and it's much easier to factor Back to factoring 2 y squared minus 8 y has 2 y in common I have I need one more factor of y though And then 2 times negative 4 would give me the negative 8 and the y is on the outside already So I don't need any insight and if I look at the next two terms 5 y and negative 20 looks like they have a positive 5 in common Five times y will give me 5 y and five times negative 4 will give me negative 20 and nice things happened because these nice little parentheses parts gave me the same thing, but we're not done because we have to Factor one more time greatest common factor That y minus 4 is my greatest common factor and then the other factor is the 2 y on the outside plus the 5 that's on the outside of the second factor or second term and That would be my factorization that I need to put over here Because I can't forget this common factor of 4 y minus 4 2 y minus 5 and this is My last answer in fact, I'm going to so highlight that so that you can see that this is what we need for an answer