 Alright, we're going to go through just a couple of examples of using what I call the AC method for factoring quadratics when the leading coefficient is not one. So the reason it's called the AC method is because our first step after of course factoring out any greatest common factors will be to multiply the A and the C values together. So in this case I will multiply six times a negative thirty five and when I multiply those two together I get negative ten. So just like before on the side I always make my little list here of what we need and we're going to need two numbers that multiply to negative two hundred ten and just like when the coefficient was one to find what they have to add to we look at the term that is the coefficient of our X or the B. In this case it's just a one. So we need two numbers that multiply to negative two hundred ten and add to one. So feel free to pause the video and do some trial and error to see if you can find the two values. But the two values that we'll use in this case are going to be the numbers fifteen and negative fourteen because fifteen times the negative fourteen is negative two hundred ten and fifteen plus the negative fourteen is one. So unlike when our leading coefficient was one we can't just use those numbers in our factors. What we'll have to do is write out the entire expression. So we keep the six X squared the same but instead of writing just X we're going to split it up and write it as plus fifteen X minus fourteen X. So notice those two added together do add up to one X but we're just separating it and then we're going to keep our constant at the end the same minus thirty five. So to factor this expression what we'll do is we'll factor by grouping. We're going to group these first two terms and these last two terms together. So here six X squared plus fifteen X we're going to just see if there's anything they have in common that we can factor out. So first I look at the number six and fifteen both have a three in common and then X squared and X both have an X that we can factor out. So I'll write that down and what I'm left with when I factor three X out of these two terms is two X plus five which I'm going to put in parentheses after it. Now after factoring those first two terms I look at the last two terms in this expression negative fourteen X and a negative thirty five. Again I just want to look to see what the two of those terms have in common. The numbers I see they both have a negative seven in common and then an X they don't both have an X so I'm just going to factor out a negative seven. And when I take a negative seven away from negative fourteen X I'm left with two X and when I take it away from the negative thirty five I'm left with plus five. And notice this isn't just a coincidence that this happened I have two X plus five in both of these terms. So the only way that this will work is if these are the same in each piece. Because when they are the same we can factor it out so we get two X plus five as one of our factors and remember when we take that piece away from each of these we are left with our second factor three X from over here and minus seven. So those would be the factors of that first expression. Now we can do this same thing with our second one. Okay just for one more example to start out we look to see if these have anything in common but there isn't a greatest common factor to factor out. So since there isn't we'll multiply our A and our C together the four and the three and four times three is twelve. So we need two numbers that multiply to twelve and then they have to add up to the B value which is the number in front of the X and in this case that would be seven. So two numbers that multiply to twelve but add up to seven while in this one it's nice and easy because it's the two numbers we used four plus three and four times three are twelve and seven. So we'll write it out just like before keep the first term the same four X squared and then to write the seven X you'll have to write it as four X plus three X it doesn't matter at all which order you put these terms in you will get the same factors. And then our last one here is a plus three. So we group the first two and the last two and the first two terms have a four X in common. So we'll factor that out and when we take away four X we're left with X plus one. Then the second grouping they have a three in common. When we take away a three we're also left with X plus one. So we have an X plus one in each piece we can factor that out and when we take away that X plus one we are left with our second factor four X plus three. And so the factors there will be X plus one times four X plus three. There are many other methods to factoring but this is just the AC method which is the method that I prefer to use when factoring.