Factorising Non-Monic Quadratic Trinomials: Common Factors


Okay! The key thing to these quadratics is to have a positive coefficient of x squared so I don’t want to have a negative in front of my x squared. So if you do have a negative, take out that negative like I did. So factorize by a negative. So this becomes positive, this becomes positive and that becomes negative, so switch around all the signs. The key thing is to have a positive in front of my x squared. But I can’t factorize any further, because there are no more common factors.

Now, 2x squared is x times 2x that’s what you put on your left, and 36, I’m going to use 4 and 9 because I know that 2 times 4 is 8 and 9 times 1 is 9 and then 8 and 9. They only have one difference which is one here, so kind of think about it in your head if you really can’t do that, you could put 9 here and 4 here and try that. But you see you get you won’t get the right answer. So, if that happens switch it around and try again.

Now, I’m gonna put a negative here and a positive here because, have a look 2x times negative 4 is negative 8 and x times 9 is 9x and you can see we want a positive x, so I’m going to put negative 8 plus 9 which makes the positive x that’s why I put the negative here. Now, as I said guys if you do ever get confused with the signs, what I would do? I put x here and 2x here. I’ll just put 4 and 9 without worrying about any signs and then you cross multiply. So 2x times 4 is 8x, x times 9 is 9x. Now, what do we want? We want positive x. How do I make a positive x with these numbers?

Well, I need a positive 9 minus 8 to make it positive x, don’t I? So I put that negative there and put that positive there. So that’s how you can think about it. If you especially with these ones with these general ones they do get really confusing later on especially with the signs. So, do what I did and then stick in the negative signs or the positive signs later on at the end like this, okay? That’s also another alternative I always find that useful as well.

It’s gonna be and keep the negative out negative x minus 4, 2x plus 9, that’s pretty much it. so you keep that negative outside like that and that’s quite possible for you to do. Can you see any common factors? Yeah, I can see some kind of I can factorize by 2 because that’s a common factor. So we get 6x squared 5x and 21. So, now it’s a little bit more simple, we just need to concentrate on this part here. So I’ll use 3x and 2x because that makes 6x squared, yeah? And 21, maybe I’ll try 7 and 3.

Again the negatives you can put in later if you’d like but if you can try to put them in them in the beginning. Because we need to have plus minus plus minus to have a negative, don’t we? And we need to have a negative here which means the bigger number should have a negative that’s why I chose 7 as being negative, okay? So, 2x times negative 7, that one, 9x and add them together, we get negative 5x, yeah which is same as this. So 2 out the front, keep that out, 3x minus 7, 2x plus 3, okay?


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