 factoring more trinomials. How do we factor something like this? 6x squared plus 17x plus 12. Now this is a simpler case in a way because we have only addition. We have no negative numbers here so that makes it one degree easier or less difficult. Now in general this is what we have. Now that formula looks awfully hard and who would like to memorize that? Again I don't recommend that you memorize any factorization formula. You will learn some as you move along. It's important that you understand what's happening and that's the only reason why I'm using this formula here. I just want you to remember usually this this middle term the linear coefficient is the one that throws people off when they're trying to factor a polynomial where the quadratic term is not 1. Let us look at it in a simpler scenario. If the area of a rectangle is given by 6x squared plus 17x plus 12 and the width is 2x plus 3 what is the length in terms of x? Now here we are already given the width given that the area is this and that the width is 2x plus 3. So now we want to know what the length is. We were already given one of the factors so this will make it a lot easier but in general you will not have that advantage. So here we need something when we multiply it by 2 we'll give us 6 that must be 3 3x and then something that when we multiply it by 3 will give us 12 that must be 4 so the length must be 3x plus 4 and how does this formula come into play? Well notice that we can rewrite this not that we want to do it but let's just to illustrate this formula a times c remember for us this is a this is b this is c and this is d. So a times c is 2 times 3x squared plus x times a times d 2 times 4 which is 8 plus b times c which is 3 plus 3 9 9 9 8 is 17 plus b times d. Perhaps it is convenient to just remember that the linear term will be a times d plus b times c but if you don't remember it just use trial and error and with time you will get a good sense of what the terms should be.