Introduction to Factorising Monic Quadratic Trinomials
Transcript
A monic quadratic basically a quadratic guy is something that has a power of two okay? So where the highest power is two. To see how in this type of expression, it has x squared where 2 is the highest power that’s called a quadratic and we are wanting to factorize that one. Now in this kind of expression, we have our x squared then our x and then some constant number at the end. So we have x squared x and then a constant number.
Always keep it in that order, okay? So don’t if it’s not in that order, I want you to first change it into that order and then work your factorization. Now in this expression, we have the coefficient, the coefficient is the number in front of any pronumeral.
Now the coefficient of x is a plus b, we don’t know what a and b are, we’re going to find that. Now it’s a plus b in the coefficient of x and for the constant term, we simply do a times b okay? Now I know that sounds a bit confusing, so what I’ll show you is the cross method. Now the cross method is something that will help you a lot when you want to factorize something like this. So try to understand this method and then you should be able to do all these types of questions.
So what you do is you simply draw a cross okay, so because it’s called the cross method and then on your left-hand side, I want you to put the factors of x squared. How do you get x squared? Well, x squared is simply x times x isn’t it? So you just need to put x here and one x here because and make sure x times x becomes x squared okay that’s easy just x and x in one of the two branches.
Now on your right-hand side, you simply look at the constant term actually I should have circled the sign in front as well. So on your right, you look at the factors of ab plus ab okay? So make sure you always keep an eye on the sign as well.
Now how do we get ab? What times becomes a b? Simply a times b, a times b becomes ab, so you put a on one and b on the other okay and they both should be positive because positive positive makes a positive okay? You could have negative and negative but I’m not going to consider any negatives because none of these have negatives in them.
If they did have a negative I would consider trying the negative ones but because it doesn’t have any negative I know that it’s all going to be positive so we don’t have to worry about the signs really much here. Now we simply multiply crossways because that’s the point of the cross method you multiply crossways, so you do x times b which is bx, and x times a which is an ax, okay?
And then you have a look at these two, you have to try and look at them and see here guys! If I expanded this, this would be ax plus bx isn’t it if I expanded it. Now ax plus bx which I’ve got here are these two the same? Yes, it is. That means you’ve succeeded and that’s the answer, so we’ve got the right thing we’ve made that equal to that so make sure your outcome when you add them you get what’s in the middle and then if that’s if that worked out then what I like to do is simply draw some brackets around here like that, so it’s going to be x plus see how these are all positive it’s positive b being positive a isn’t it? So do x plus a times x plus b here and this will be your final answer.
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