 This video is called Factoring When A Equals 1. A in this case is the number or the coefficient in front of the X squared. So when A equals 1 there's really an implied 1 here. So now to factor something like this, the first thing you'll ask yourself is can I take out a GCF? So you'll look and see well nothing can divide out of 1, 7 and 12 that's bigger than 1 and I can't take out an X because I've got X's in this term. I've got an X in this term but I don't have anything here. So finding out that, so taking out a GCF won't help me much at this point. So what I'd like to do is ask myself what multiplies to give me 12 and adds to give me 7. So let's make a list of things that multiply to give me 12. I've got 12 in 1, 6 in 2, 4 in 3. So those combinations multiply to give me 12. Do any of them work to add to give me 7? Well 12 plus 1, there's no way that could add or subtract to give me 7. How about 6 and 2? I don't think there's any way that those could add or subtract to give me 7. But if I have a positive 4 and a positive 3, those will add to give me 7 and multiply to give me 12. So what I'm going to do is factor this into two binomials where the 4 and the 3 go in the second slots each. Now I have to spend a second and make sure that 1 X squared, that could be broken, oops sorry, that could be broken down to X and X. So I'll put the X and X in my first slots. We decided the 4 and 3's were positive so that would be my factored answer. Now let's go ahead and check our answers. We'll do some foiling first, outside, inside last, X times X is X squared, X times 3 is a plus 3 X, 4 times X is a plus 4 X, and 4 times 3 is a plus 12. When you combine those like terms in the middle, you get back to where you started. So this gets us back to the beginning so we know that we factored correctly where the quantity of X plus 4 times the quantity of X plus 3 is our factored answer. Let's try three more. So this one, G squared plus 7G plus 10, we know we can't take out a GCF because I don't have a G in all three terms. Remember there's an implied one here, I can't divide out anything bigger than a one so there is no GCF to take out. So let's start by thinking what multiplies to give me 10 a positive 10 and adds to give me a positive 7. We'll start by making a list, what could multiply to give me 10? The only ones I can think of are 10 and 1 or 5 and 2. Is there any way that 10 and 1 could add to give me a positive 7? I don't think so, but there is a way if 5 is positive and 2 is positive that can add to a positive 7 and multiply to a positive 10. So it's time to make my parentheses. The G squared can break up to G and G and then I'll put a plus 5 and a plus 2. Now you have another option of how you'd want to write this. If you wanted to put the plus 2 first and the plus 5 second that would be fine. Either of those answers would be considered appropriate and correct. D squared minus 17 D plus 42. So again ask yourself can I pull out a GCF? I don't think I can because I don't have a D in all three terms and since there's a 1 here there's nothing I can divide out that's bigger than a 1. So start asking yourself what multiplies to give you a positive 42 and adds to give you a negative 17. Well you'd have 42 times 1 7 times 6 gives you 42 21 times 2 gives you 42 and so does 14 times 3. So we need to pick which one will add to a negative 17. Well I don't think 42 and 1 there's any way to add to negative 17. 7 and 6 that would get me to like a 13 or negative 13 not quite enough. 21 and 2 would only get me to a 23 or a 19 but I see it. 14 and 3. Now here's the thing a positive 14 and a positive 3 would give me a positive 17. I need a negative 17 so a negative 14 plus a negative 3 that's what adds to a negative 17 and multiplies to a positive 42 because negative 14 times negative 3 is positive 42. Negative 14 plus a negative 3 is negative 17. So there is our choice. So make your parentheses. The d squared becomes d and d and you can put a negative 14 and a negative 3 in the slots. Remember it'd be okay if you reverse these and had the negative 3 over here the negative 14 over there. So this would be your factored answer. M squared plus 6m minus 27. I can't take out a GCF because I don't have a letter in all three terms and I can't take out any numbers because this term the biggest one is the biggest number the number I have is 1. Sorry about that. So immediately start asking yourself what multiplies to give you negative 27 and adds to give you 6. So make a list of the factors of 27. What could multiply? All I can think of is 27 and 1 and 9 and 3. Well 27 and 1 there's no way that that can add up to a positive 6 but is there any way 9 and 3 could add up to a positive 6? There is a positive 9 and a negative 3. So we have a positive 9 times a negative 3 is negative 27 and a positive 9 plus a negative 3 is a positive 6. So I found my solution. Sorry about that. Got excited. We make our parentheses. The m squared becomes m and m and I'm going to go ahead and put the positive 9 here and the minus 3 here that would be my answer and I am I think this time going to check just to make sure I did everything correct. So when I foil and combine like terms I should get back to where I started. m times m is m squared. m times negative 3 is negative 3m. 9 times m is a plus 9m and 9 times negative 3 is negative 27. So you end up with m squared plus 6m minus 27. Ask yourself is that where we started? Sure enough m squared plus 6m minus 27. I really would highly encourage you to do this extra work down here when you're doing problems like this especially on a quiz or a test because it just confirms if you got things right or wrong. And I'll tell you it's very easy to mix up where the positives go and where the negatives go and lots of students goof the sign part up. But by taking the time to do this work by getting back to your original answer you know you did your positive and negatives correct. If you don't get back to the original that tells you something's probably wrong with those positive and negatives and it's worth a second look if you want to get the answer right. Happy Factory!