Introduction to Factorising Non-Monic Quadratic Trinomials
Transcript
See here! This time we have acx squared in the beginning so a time some number c will be our factors or the coefficient of x squared and here we have a d, so a times d plus b times c in the coefficient of x and then finally constant will be b times d.
Now I know that looks a bit confusing but you’ll get the idea when we get to the questions. Have a look this time there’s no common factor so we can’t actually factorize it like we did in the mnemonic polynomials quadratic sorry. So this time, acx squared that will be ax times cx. x squared is still x times x but ac this time will be a times c, so we have to put ax and cx. It’s not just going to be x and x this time, and here we just do our b and d again.
But have a look guys when I cross multiply, I get ax times d which is adx and cx times b which is bcx and if I add that up I’ll get bcx plus adx, and if I factorize that by x this is what I’ll get which is exactly the same as the middle. So we do the same kind of thing but it just still takes a little bit more of a step, okay? So because it’s not because it’s got extra coefficients in front of the x.
So see how we still compare this with the middle part and if it’s the same we’ve got the right combination, so you do ax plus b and cx plus d, okay? That’s the idea. So we put it’s not just going to be x, it’s going to be ax and it’s not just going to be x here, it’s going to be cx. That’s the difference. Let’s go into the question and I’ll show you exactly what we do by using the cross method again so we always stick to the cross method. Okay! So this one, it says 2x squared plus 7x plus 3.
Now what I want you to do guys is first think to yourself. Are there any common factors? Now this one it doesn’t have any common factors so we can’t factorize. So we’ll start with our cross method but I’m going to put 2x and x because 2x times x makes 2x squared, doesn’t it? So it’s not just going to be x and x. It’s going to be 2x and x. Now on my right-hand side, I look at the factors of 3. It’s going to be 1 and 3. I’ll put 1 here and 3 here.
Now this one is not very straightforward. You don’t know if you put 3 here or one here, you don’t really know. Just put it into someplace and try and do some trial and error okay? At the beginning, you might have to do some trial and error. But the reason why I put three here is because when I cross multiply, I know that two times three is six and one times x sorry two x times three let’s actually try the com cross method. x times one is x, two x times 3 is 6x. So because 2 times 3 is 6 and 1 times 1 is 1. I know that when I add them, I’m going to get 7, 7x yeah.
That’s why I put 3 here but sometimes it’s a little bit difficult to tell that. So you might like to do some trial and error. You might like to start by putting three there and if that doesn’t work out, you might like to switch that and try again, okay? So don’t panic if you don’t get the right answer. Always trying to switch around and try again. So that’s what I’ve got and I know that these two are the same. So I’ve got the right combinations. So it’s going to be 2x plus 1 times x plus 3 just like that, okay?
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