in this video we're going to look at another example of factoring using the AC method so let's remember the first thing we need to do is look at our trinomial and be clear about what the values of a B and C are so in this trinomial a is 4 B is 37 and C is 9 now you got to make sure this trinomial is in order if you don't have your x squared term first you definitely want to do that for example if if the problem was given to you like this 37 X plus 9 plus 4 x squared you would want to rewrite it in order with your x squared term first then your X term then your 9 term rewrite it like this before you even start sometimes books or problems can be tricky like that they'll throw one that's out of order and make sure you know you have to put it back in order alright so let's get started the first thing we need to do is determine the value of a times C so 4 times 9 which is 36 so we'll write that down 36 we're going to make our little puzzle-solving chart over here just like this red thing this is kind of like your formula this red thing and we're going to create a similar diagram based on our particular problem so a times C and our problem is 36 4 times 9 is 36 and B is 37 so for this particular problem we need to figure out two numbers that multiply to be 36 and add to be 37 so you could write out the things that multiply to be 36 you got 1 times 36 well there it is right there right 1 plus 36 is 37 and and I'll tell you if you know when you have all these as pluses that means everything is going to be positive we need to multiply to be a positive 36 and add to be a positive 37 so these two numbers have to be positive if this number is one more than this number if your B value is one more than your a times C value then it's always going to be 1 times whatever your AC value is so we kind of lucked out on that one but you know if you kept going here you'd have three times 12 and 6 times 6 and 18 times 2 and none of those would have worked we kind of stumbled on it here all right so let's go ahead and do our next step which is to rewrite our trinomial up here by splitting the middle term so we're going to take this 37 X but we're not going to write 37 X on the next line we're going to write 1 X plus 36 X using our two numbers from the box over here so the four x squared comes down the 37 X is going to get split up and it really doesn't matter I mean you could if you had the 1 or the 36 first you could have the 1 X and then the 36 X it really wouldn't matter in this case so I'll just do it plus X plus 36 X plus 9 so in that step we took our 37 X and we split it up into 1 X plus 36 X which is the same as 37 X and the reason we did that is so we could create four terms and create a factor by grouping problem and now we just solve it like a factor by grouping problem so 4 x squared plus X the greatest common factor of those first two terms is X and we when we take that out we have 4 X plus 1 and you can distribute this X to double-check that plus the greatest common factor of 36 and 9 would be 9 then we'd have 4 X plus 1 and luckily we know we did this right because what's left in these parentheses is the same and that should always happen when you're doing factor by grouping if it doesn't then that means one of two things number one you could have made a mistake or number two the trinomial is not factorable it's one of those two things so the first thing I would do is go back and make sure I didn't make a mistake okay so last step whatever was underlined here whatever the common binomial is in these parentheses we write that down just once and then we write down whatever is left whatever is not underlined which is x plus 9 and we are done if I'm on a test and I'm doing this and time is of the essence I don't have a lot of time I'm probably going on to the next problem if I feel like I'm doing good with time I have a little time or it's the end of the test and I'm looking over my tests I'm going to check my answer and the way we check it is by foiling it back together so let's just do that I think we have enough room here so to check that I'm going to do foil and if I foil these two binomials together I should end up with the original trinomial 4x times X is 4x squared 4x times 9 is 36 X 1 times X is 1x or just X and 1 times 9 is 9 and then I can combine my middle terms 36 X plus 1 X is 37 X plus 9 is my original problem so I feel good about that right and this will be my final answer