Factorising Non-Monic Quadratic Trinomials: Mixed Signs

Factorising Non-Monic Quadratic Trinomials Mixed Signs
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Now 30. I’m going to do the same thing, 7x squared that will be 7x times x. I put x and 7x onto my left-hand side. The reason why I’m doing that is because I can’t factorize any I can’t I don’t have any common factors, so I have to stick to this. And then six is two and three and one and six but I’ll try to use negative two and negative three, two and three.

And you know why I’m using the negative, don’t you? Because this is a negative. If this is negative and this is a positive always use your negative negative yeah. Now the reason why I put 2 here is because have a look! 7x times negative 2 is negative 14x and x times negative 3 is negative 3x. And I know that 14 and 3, they do make 17, don’t they? So when you start guys kind of think to yourself on the top of your head. Think about it think about what they will add up to, okay? And then you kind of imagine where the right place would go. So now negative 14 minus 3 is negative 17x which is exactly the same as that. So that’s pretty much it. x minus 2, 7x minus three, okay? So that’s the idea, guys.

So I’m going to do the same thing. x and seven x on our left-hand side and fifteen, five and three, one and fifteen. I’ll try to usually like to try all the ones that as close together like five and three and I know that seven times three is going to be 21. I know that if I add five, I’ll get 26. That’s why I’m going to put three here and I’m going to put the 5 here and you know why I’m putting the negative negatives here right because that’s negative and that’s positive. So 7x times negative 3 is negative 21x, x times negative 5 is negative 5x, okay?

And even if I didn’t have any of those signs there guys, you can see that to make negative 26. I need to have negative 21, minus 5, don’t I? So you can think about it like that and put in stick in the signs afterward like I did. And then now negative 21 minus five is negative 26 which is that. So going to be x minus three times seven x minus five, that’s the answer. 2x squared so x and 2x like we always do.

Now five the only factors are one and five but I’m going to put negative one and five like that and again guys signs don’t worry too much about that you can always put that in at the end if you like. So I’m going to put one here and five here because we need three, yeah. If I put five there, I’d get ten that’s too far away from three, so that’s why I’m going to put 5 here and 1 there because I know that 2x times negative 1 is negative 2x, x times 5 is 5x and I know that 5 minus 2 makes 3, so we get 3x. So it’s simply going to be x minus one, two x plus five, just like that, okay?


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