let's go ahead and get started so the main thing I want you guys to take away um from at least when we worked on our unit on factoring is that all Factory all products are trying to all China almost can be factored into a product of two binomials so we might have trouble with factoring but hopefully we can at least go with this point that we know that this trinomial can be factored into a product of two binomials now um you know I know there's a lot of different techniques you guys learned and you know algebra and Algebra 2 to like figure this out but we in this class we kind of need speed so we need to really think about this and be able to do this efficiently and I can tell you that majority of the problems that we're going to be doing in this class that do involve this method are going to be rather simple so therefore I want to kind of think about this how I treat this to doing this in my head for quick speed because obviously if you can't figure it out some of the methods you have previously learned work perfectly fine they just take a little while so if we remember that the product of two binomials via distributive property or you may remember it as foil the first two terms are going to give you that first term in your trinomial so 2X and X needs to give you 2x squared which it does now we need to figure out what two numbers multiply to give me two well thankfully we don't have many options here we have two and one and negative two and negative one right and obviously since our middle term is going to be positive that means our two factors need to be positive and then really guys it's either a 2 is going to go here a one's there or a one's there and a twos there and the main thing that you need to think about is your inner and your outer terms need to combine to give you a 5x so obviously if I do a 1 here and a 2 here what we notice is so 2x times x is 2x squared 2 times 1 is 2. however 2x 2 times x is 2X and then 2x times 1 is 2x well 2x plus 2X is 4X we need it to be 5x so in my brain I can kind of look at that and say well if I just switch this around that gives me 1X that gives me 4X 1s plus 1X Plus 4X is 5X and there you go now the next thing though again it's not factoring so if you want me to check your homework make sure you didn't just Factor it because that's not what the question is asking the question is asking to solve so therefore we need to apply the zero product property if we have a product equal to zero then one or more of the factors has to equal zero so therefore we can set each factor equal to zero and then go ahead and solve subtract the one divide by two subtract the two and those would be your solutions to the quadratic okay so make sure you take that extra step that's one of the big things that students are not to receive