Breaking Down Barriers in Algebra with Monic Quadratics + –

Factorising Monic Quadratic Trinomials Plus Minus Form


Now again, it’s a bit different because now we have positive here and negative here, but don’t worry too much about this number, guys, because the the first thing you should consider is the factors of this one. Okay? Now it’s negative again. How do we make negative? Well, we need to have plus and minus, don’t we? Plus times negative makes negative. So again, it’s going to be one of one plus and one negative okay?

Again, I’m going to start with my x and x and then think about 56. I’m gonna try to use 7 and 8 again okay? Because that’s the one I can think of at the top of my head, and we want this plus one x, isn’t it? I know that the difference of these two numbers is one. So, this time, we need a positive one. How do we make a positive one with these numbers?
Well, I can say plus 8 minus 7 makes plus 1, doesn’t it?

So this time, I’m going to have minus 7 and plus 8. Draw your cross x times negative 7 is negative 7x. X times 8 is 8x. Negative 7x plus 8x is 1x or just x. Positive x, which is the same as what we have here, I’ll rub that off. Yeah, we’ve got the positive x. So the answer is x minus 7, x plus 8, okay?

Remember there’s a plus there isn’t it? 12, okay? Again! We’ve got a plus here and a negative here, but again, don’t worry too much about this one. Let’s find the right factors first and then see if we get that, so again, I’m going to put my x and x on my left. 48, what do you think? Well, I’m going to try and think of some factors, though again, 48 has a lot of factors, yeah? Like, I don’t know 4 and 12 and 6 and 8, but I’m going to actually use 6 and 8 because the difference is 2. That’s what I want, isn’t it? But I need to make, make sure this time this is negative. It’s going to be plus and minus in one of them, isn’t it?

So, How do I make plus 2 with these numbers? Minus 6 plus 8 would be positive, isn’t it? Ok! So plus 8 minus 6 makes plus 2. So that’s where I put the negative, that’s where I put the positive. If you do what if you did what I did before, you’d probably end up with a negative two, which is wrong. So I’m gonna put my negative 6 here and plus 8 there and then cross it. Negative 6, cross it 8x, negative 6x plus 8x is 2x which is exactly the same as what we have here.

Our answer is x minus 6, x plus 8, and that’s the right answer. This is your final answer.
okay? So when we multiply those two factors together.

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