if you're struggling with factoring quadratic trinomials ax^2+bx+c like this where the leading coefficient here is not equal to one then this video is for you because I'll show you five easy ways to do it the first way is called the AC method with grouping this is the a this is the C we first multiply a and C together 6 * -3 we get -8 then we have to think about two numbers that they multiply to8 and when we add them we get positive 7 and the correct combination is 9 and -2 but if one of the numbers is negative write it down first so put on -2 and 9 we do multiply get -8 and when we add then we do get seven and this will allow us to do the following we keep the 6X s but for the 7x we will break it down as -2X plus 99x this is still 7x and then of course that will still have the minus three now we have four terms we can do this by grouping the first two and then the last two 6 and two we can Factor on two x squ and x we can Factor on x 6 divided by two would get three x² / X would get x to the 1st- 2 2 / 2 is min-1 and the x is out already so that's what we have then put down the plus 9 and three we can factor of three 9 / 3 is three and then X still right here neg3 / 3 is minus one now as we can see this and now the same we can factor that out and then you have 3x - one just put it down one time yeah we took it out at the second factor is this and that so 2x + 3 and got that for the second method it's pretty much the same thing it's called the AC method with the Box we still do a * C and get 18 and we still need -2 and 9 to get seven and now we are going to first draw a box like this and then we are going to cut it like this for this right here go ahead and put down 6x squar for this right here go ahead and write that down - 2x and then also the 9x this and that gives us the 7x lastly we have that minus 3 now just look at the top row six and two we can factor a two x squ and x we can Factor an X done with that now bottom row 9 and three we can factor out three this has X this does not so can I factor out the X and in fact we took out a positive three right so plus now do the First Column 6 and 9 we can Factor on three x squ and x we can Factor on X here - 2x - 3 we can factor a minus one so the answer is just this right here 3x - 1 and then the other one 2X + plus three of course if you switch the water of the factors doesn't matter that's it now for the thir method it gets a little bit weird we still need to do a * C and get 18 and we still need -2 and 9 to get a seven check this C let me just proceed instead of do this by grouping with draw the Box we first just draw two sets of parenthesis and then you see here we have 6X s right just go ahead and write down 6x and 6X trust me works and then let's go ahead and enter min-2 and then + 9 all right now what though notice I didn't put on equal sign because this is not equal to this but check this out here we have 6X and two 6 and two we can divide by two we can reduce that by two and then we will get 3x minus one first Factor 6 and 9 we can have a common factor three we can divide this by three likewise do the same thing divided by the common factor and then this right here we get 2X and then right here we get plus three I can tell you this is equal to that and then we're done this is just like intermediate step now for the next way you might be thinking it doesn't make sense either but let me tell you it also works this right here it's called a slide and divide I also call this the Amazon Prime way because you do this again it's a Time C once again right but anyway though you just go ahead and put a six multiply with the3 and then you will have X2 + 7x and a minus 18 again this is not the same as that but just trust me at the end we will get the correct factoring now what though well this is so much easier to factor right it's just a coefficient one here so it's just x and x and what do we need we need minus 2 and posi 9 in order to get what8 and then when we add it we get seven now what check this out if you do it this way then what you want to do is divide this by six because we didn't use it divide it by six and then divide this number by six as well 2 over 6 can we reduce that yes if we reduce that we get 1/3 isn't it but we still have the three we are going to put a three here let's try this 9 over 6 right reduce that by we get 3 over two and then we have a denominator so put a two right here and now tell you this right here just just ignore the middle now because I can tell you the answer is 3 x minus 1 * 2 x + 3 and then we are done and this is equal to that done and now for the last way I think it's the most straightforward way and that's also the method I use for teaching my students I call this the Tik toac toe method what we want to do first is just dra the Tik Tock to boxes like this and then you are going to ask yourself what * 12 give us 6 x s and the correct combination is 2X and 3X now move here and then you have to ask yourself what times what will give you3 well you can have1 and three or maybe three here negative one right I don't know let's just go ahead and put down negative one here and three here I have no idea this is the check you take this times that you put it here 6X and then you take this multiply by that you get 3x 6X minus 3x do we get 7 x no in that case that means we didn't get the correct combination so what that means is don't worry just try again the correct combination for this is we put a three here And1 here 2x * 1 we get -2X 3 * 3x is 9x together we do get a positive 7 x now when we write down the answer we read it across 2x + 3 time 3x - 1 just like this let me know which way you like the most