hi everyone this is mr lam here just going to go over the guess and check method for those of you who need a quick review on it but before we go in the guess and check method we need to refresh our memory on multiplying binomials so if we have two binomials here three x plus four times four x minus one and we foil those out uh foil just meaning multiply these we would multiply the three x times the four x which is twelve x squared then we would multiply the 3x times the negative 1 which is negative 3x and then the positive 4 times the 4x which would be plus 16x and then lastly the positive 4 times the negative 1 which would be negative 4. then to simplify this further we look at our like terms which are right here in the middle we can combine those like terms and we would get in our final answer 12x squared negative 3x plus 16x is plus 13x minus 4 and this would be our final answer now one thing i want you to notice is if you notice the red number right here is always this number times this number and the blue number at the end always is this number times this number and then you're just trying to figure out this middle number here when we factor so let's practice factoring using the guess and check method so the first thing we want to do is we want to list out the factors of 3x squared so i'll do 3 times 1 and there's no other factors of three so i'll just leave it at that and what are the factors of six well i know it's positive six so it's one times six or three times two now we know there's going to be two binomials here and the first terms in each binomial are going to be the three and the one so we're going to put a 3x here and a 1x right here then the next step is is we choose between either this factor or this factor to go in the other two spots right here now because we have a positive middle number and a positive last number we know the two numbers are going to be positive so the one condition that you must remember is that you cannot place any number here that you can take a gcf out with the three so for example if i put a 6 here that is not allowed because 3 and a 6 have a common factor which is 3. so you can't put a 6 there so the only one i would be able to put there is the 1 which means the 6 would go here now when you look at these i draw these two arcs here 1 times x is 1x and 3x times 6 is 18x now the question is is with these two numbers 1x these two terms 1x and 18x is there any way that i can get positive 11 x is there any way i could get positive 11x with those two numbers and the answer is no so actually the 1 and the 6 will not work in here so what i do is i erase that erase that and let's try a new number let's try the 3 and the 2. that's our only other option well i know a 3 cannot go in here because there's already a 3 there and you can take a 3 out of that binomial so it must be a 2 here and a 3 here now when i do 2 times x that's 2x when i do 3x times 3 that's a 9x is there any way i can make 11x with that 2x and 9x absolutely if they're both if they're both positive so i'll go plus plus and this would be my final answer a good way to check this to see if you're correct is if you multiply this it's 3x squared multiply this just foil it out plus 9x multiply 2 times x is another two x and two times positive three is plus six combine these like terms together you get three x squared plus eleven x plus six does that match our original answer yes it does so that is correct all right so now to go to the second problem uh what i like to do again i forgot to do this in the first problem is always check to see if there's a gcf that you can take out and it doesn't look like there's any other gcf you can take out besides one so then let's just list our factors for two is two and one and the factors of twenty there's a lot one times twenty two times ten four times five and i think that is about it so now we're going to draw our two binomials and we're going to put the 2x and the 1x in the first spots now the next step is to choose one of these now i'm i i don't think it's going to be 1 times 20 now maybe it is but i'm going to guess maybe it's either 2 and 10 or 4 and 5. so let's just try four and five that seems like a one that it could be now if i use four and five i can't put four here because the four and two have a two in common so the only thing that could go there is a 5 and that means the other one's a 4. and so let's multiply these 5x and 2x and 4 is 8x now the thing is is i know that one of these terms has to be negative because i'm getting a negative 20 right and the only way to get a negative 20 when you multiply numbers is if one is positive and one is negative now i got a 5x and an 8x and my goal is to get this negative 3x right here now is there any way that i can get negative 3x with 5x and 8x actually there is if 8x is negative right here 5x plus negative 8x is negative 3x which means this needs to be negatives 2x times negative 4 is negative 8x and 5 is positive so there's my final answer right there all right going on to moving on to number three let's take out look at this one all right so it's going to get gradually harder as we go but let's look to see if there's any gcs between these three terms there's no number that goes into all three so let's just list out the factors six and one three and two and then the nine is either nine and one or three and three so i'm going to make my two binomials here and let's just use i'm going to use the three and the two so i'm going to put 3x and 2x and then i'm going to try to use the 3 and the 3. well if i put a 3 here i can't put a 3 here because the 3 x and the 3 have a 3 in common which means it's a 3 and a 3. so i can't use that one so that one definitely doesn't work so how about the 9 and the 1 well i can't put the 9 here because it you can bring out a 3. so i'm going to put a 1 there and a 9 there and let's kind of see if our arcs can get us to positive 25x so that's 2x and that's 27x and my goal is to get us to 25 x positive 25 x i know one of these has to be negative because this is a negative nine so oh i think i can't get to positive 25 x if this 2x is negative so how do i make the so i have negative 2x plus 27x is equal to 25x which checks so how do i make this a negative 2x i would put a negative there a positive there and ladies and gentlemen there is my answer all right going on with number four we're getting pretty tough here so let's look if there's a gcf first step is gcf there is no gcf so let's just list the factors of 12 1 and 12 2 and 6 3 and 4. uh and seventy one times seven seven times ten and i think that's it it's not much more unless i'm missing one so then these numbers are quite large so let's uh let's not go 1 and 12. let's pick the i like the three and the four let's go to the three and the four so we go three x and four x um and then um one and seventy probably not i'm gonna do the 7 and the 10 so the 10 can't go here because the 4 and the 10 have a 2 in common so a 7 must go here and a 10 must go here so if i were to go like this i would get 40x and if i were to go like this i would get 21x now the question is is can i get 61x here i can get 61x if they are both positive which makes sense because the sum is positive and the product is positive so these would both be plus and we have our answer right there all right guys the last one we're going to do here is number five all right so first thing we do is see if there's a gcf oh i actually think there is a gcf of 10 68 and 48 a 2. so let's take out a 2 and then we get 5 x squared minus 34 x plus 24. again this is this reverse distribution right taking the gcf out if i multiply distribute that 2 to everything it's going to get me this up here so now what we're going to do is we are going to factor this portion uh we are not going to worry about all this right here because we took a 2 out but we're going to worry about the what's in the parentheses so different ways i can get five x squared is five and one the different ways i can get 24 are one and twenty four two and twelve four and six and three and eight all right so let's write our two binomials here i got five x and one x now what numbers could i try um let's just try 2 and 12. see if that works okay so if i put a 2 here and a 12 here i get 2x and 5 times 12 is 60x well i know that my goal is negative 34x and there is no way with these two numbers that i can get a negative 34x you'll notice the product is positive 24 and the sum is negative 34 which means both numbers are going to have to be negative because if you multiply two negatives you get a positive and if you add two negatives you get a negative so it's definitely not these two however is it possible that this could be 12 and this could be two well that would give us 12x and that would give us 10x that will still not get us negative 34x so we can completely eliminate the 12 and the 2. how about the 4 and the 6 let's try the 4 here and the 6 here well we get 4x here and we get 30x here hey i could definitely get negative 34x if they were both negative which is what i want so i go minus minus now the last thing you have to do is you have to bring this 2 down in front and this is your final answer all right everyone well hopefully that made more sense but again it's just listing out factors and going through the process of guessing and checking numbers seeing if they work or not thanks and hopefully this was helpful bye-bye