Factorising Monic Quadratic Trinomials Minus Plus Form

Transcript

Again I’m going to put x and x on the left-hand side because again x times x is definitely x squared. Now 3, 3 is simply 3 and 1, isn’t it? 3 times 1 is 3. But when this is a plus and this is a negative we need to make negative don’t we? So what you need to do is consider some negatives. What makes it positive? Well, positive 3 times positive 1 makes positive 3.

What about negatives guys? What about negative 3 and negative 1? Negative negative is positive, isn’t it? So therefore negative 3 times negative 1 is also positive 3. Now what I’m going to do guys try to use this combination because I’ll put negative 1 here and negative 3 here, watch what happens. Now I’m going to try x times negative 1. Which is negative x? x times negative 3 which is negative 3x. Now if I add them I get negative x plus-minus 3x. Plus-minus is negative, so minus x minus 3x is negative 4x which is the same as the middle okay? So when this is a plus and this is a negative, you must change these to both negative.

Does that make sense? So that’s where you’re going to consider a little bit more on the negative parts, so negative x minus 2x is negative 4, so I’ve got the right combination, you draw the brackets. This time it’s going to be x minus 1 times x minus 3. Okay? See the difference? So it’s not that hard it’s just a little bit different because of the signs. Okay? x and x on the left now 6 guys again this one it’s 1 and 6 or 2 and 3 isn’t it? Again we have two sets of factors but which one do you think you will use that. Okay.

First of all, this is a negative. Now again it’s negative so I’ve got to put my negatives in front yeah because negative 2 times negative 3 makes positive 6, negative 1 times negative 6 makes positive 6 as well. Okay? But because this is negative I have to put negatives on all of them. Now guys because it’s negative 7, I’m actually going to start by using this one I think that’s pretty much the answer because negative 1 minus 6 makes negative 7. So I’m going to start by putting negative 1 here and negative 6 here. Draw your cross, x times negative 1 is negative x and x times negative 6 is negative 6 x and you can see that negative x minus 6x is negative 7x which is exactly the same as what’s in the middle, so I’ve got the final answer. So draw your brackets. It’s going to be x minus 1, x minus 6, okay? And again guys if you do have the time you can expand that out and just see if that makes the same as that one okay, so that’s the answer.

Seven. Okay. Same kinds of thing. Put x is on my left and 12 guys, what do you think? I won’t write down all the factors but you guys can tell me. What are the factors of 12 that would make negative 7 if I added them? I think what about 3 and 4? Well I’m gonna have negative 3 and negative 4 yeah negative 3 and negative 4 because I know that negative 3 times negative 4 is positive 12. So I’ll put negative 3 here and negative 4 there. Cross it. x times negative 3 is negative 3x, x times negative 4 is negative 4x and if I put them together, negative 3x minus 4x is negative 12 x is not true oops pretend you didn’t see that that one should have been a 7. I don’t know sometimes we have a mistake.

So negative 3x minus 4x is negative 7x definitely isn’t it? And you compare it with the middle, you’ve got the same thing. So, therefore, I’ve got the right choice I’m going to put my brackets and we’ve got x minus 3 times x minus 4. Okay? Now guys can you tell me the factors of 10 that would make negative 7 when I added them up? What about 2 and 5? 2 and 5. Now I’m gonna of course put my negatives in front okay because that’s a plus and that’s negative. So I’ll put negative 2 there and negative 5 there. x will start with this one x times negative 2 is negative 2x and x times negative 5 is negative 5x. Put them together. Negative 2x minus 5x is negative 7x which is the same as that one.
So we’ve got the right choice, so it’s going to be x minus 2 times x minus 5. okay?

 

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