 The simplest example of a complex trinomial is of the following form ok this is the one I usually start off with. So the simplest form is 2x squared plus 5x plus 3. Now the way this works is if you've got something like this the first thing you would do is look for a GCF where you can take out a 2. Now in this case you can't take out a GCF you can't take the 2 outside the bracket you know put a bracket there where you can get the x squared by itself ok. So this is the way you end up factoring is you can use the quadratic formula but if you know if it's easy it's quicker to do things manually if you get things that are simple like this ok. So the first thing you do step number one for complex trinomial factoring is you take the 2 and you multiply it by the 3 and you drop it from the next statement ok from the next step. So you're going to grab the 2 multiplied by 3 and that number replaces your c term and you're going to drop the 2 whatever the number was in front of the x squared. So your next line becomes so now you got x squared plus 5x plus 6 ok this now becomes a simple trinomial we can factor this and this is one of the first things we factored in the simple trinomial section right. So all you do you put your brackets in and if you factored there's two numbers that give you 6 multiplied to give you 6 and have to give you 5 that's 2 and 3 we've already talked about this. So what you do is positive 2 and positive 3 so you're going to go plus 3 plus 3 those are your two numbers in there the x squared you're going to break down into x times x so this is step number 2. Step number 1 you take the 2 multiplied by the 3 drop the 2 in the front and you have your you replace your c with whatever the multiplication of those two terms were. Step number 2 you factor you know just simple trinomial because as soon as you do that it becomes a simple trinomial your next step is a simple trinomial right so step number 2 is you factor your simple trinomial the way you factor simple trinomials right. Step number 3 you take the number that you took the coefficient in front of the x squared and you put it back in front of the x terms after you factored simple trinomial so the 2 here gets dropped back in here. So right now you're going to have 2x and 2x so you got 2x plus 2 2x plus 3 okay. Step number 4 you look at both these terms okay and you take out the GCF and you dump it you get rid of it okay and this is the only time where when this is equal to 0 and we'll get into it when we're trying to solve for it the dumping part makes sense because all you do you factor out the GCF you bring it out here and you divide by you know the term in front whatever the number is and you divide the other side since this is 0 0 divided by number is just 0 right so it gets rid of it when it comes to the factoring keep this in mind this is the only time where you can take out the GCF to the front and dump it so what you have now there's a GCF here the GCF for 2x and 2 is just 2 so you're going to take out the 2 it comes up to the front and you dump it okay so your next line becomes so if you take out a 2 from this that's just x if you take out a 2 from that that's just 1 so this becomes x plus 1 now you can think about it there's a 2 here right now but it's going to be you're going to get rid of it right so there is a 2 you took the 2 out but it's dumped so you take out a GCF from here and you take out a GCF from here and if there is no GCF that term remains okay so there is no GCF between the 2x and the 3 so it just becomes 2x plus 3 now this x plus 1 times 2x plus 3 is the top guy factored if you multiply this out you're going to end up with that term right there now a full foil this out right so this is the four-step method step number one take the coefficient the number in front of the x squared and multiply it by c drop it in the next term and whatever the number was that you multiplied it by becomes your c term factor your second line just the same way you would a simple trinomial because this it is now simple trinomial you took the coefficient in front of the x squared and put it with the c right you could factor that out step now step number two step number three you take whatever it was that you factored out and you drop it back in front of the x terms in your factor of the simple trinomial from there you take out a GCF and dump it and whatever your room whatever remains whatever you end up with is the top guy factored okay it's as simple as that it's brilliant little algorithm I guess it's it's it's automatic you don't even have to do any thinking right just take the number and multiply that out factor that out but the number back in GCF out dump it that's your that's that's your fact that's your complex trinomial factored at the bottom we'll do a couple of more examples it's again it's a really simple method but we'll end up doing a couple more examples and hopefully make sense and you should try you know you should try this technique on a lot a lot of examples if you if you're gonna do you do a fair bit if you're gonna get good at this you should be able to you know do a fair bit of practice and again when it comes to factoring trinomials or anything factoring anything you're gonna have to know your multiplication table because you know we talked about this in the simple trinomial section super important to know your multiplication table because you're looking for two numbers that multiply to give you C and add to give you the middle term and your multiplication table you start off with that one because there are there are less combinations of now integers to multiply give you six then there are that add to give you five okay there's an infinite number of these there there isn't an infinite number of integers anyway that multiply to give you six but there's an infinite number of integers that add to give you five okay so you always start off with the multiplication and you look for your two numbers through the multiplication and test to see if they equal the you know the coefficient in front of your middle term and one thing to keep in mind is whenever you get a trinomials like this you want to put it with decent descending order so your highest order X goes in in you know it's your first term is it goes in the front and then decreasing order coming down