Learn how to find factors in algebraic expressions. Knowing how to factorise is an important skill for higher tier GCSE.
Transcript:
This video is going to use the following exam-style question to show you how to answer GCSE questions involving the factorisation of algebraic expressions.
So, in this question, we are asked to circle the factor of the following algebraic expression, and are given four possible answers.
Now, to answer this, I want to start with a quick recap over here on the right about what is meant when we are asked to find a factor.
And this is easier if we think about numbers first, and then use this knowledge to help us deal with the more complicated algebra based question over here on the left.
So I’m going to start with a number, say 6, and underneath I’m going to write a list of its factors which are 1, 2, 3 and 6.
Now these are the factors of 6 because they all divide into 6 exactly.
So when we divide 6 by any of these numbers there is no reminder. For example 6 divided by 2 is 3, or 6 divided by 6 is 1, etc.
And it is for this reason that factors are sometimes called divisors because they divide exactly into the number you are given.
And so to relate this to the algebra based question here, I want to point out that a property of factors is that when we multiply certain pairs of them together we get back to the number we started with.
So here we have a pair of factors, 2 and 3, and when we multiply them we get 6.
And in a similar way 1 times 6 equals 6, so this is another factor pair.
So how can we use this knowledge to answer this more complicated factorisation question?
Well let’s have a go here underneath, and I’m going to start by highlighting the two terms in the algebraic expression we’ve been given.
This is because we need to identify either a letter or number that is common to both of these terms; i.e. a number or letter that divides into each of these terms since this will be one of its factors.
So here we have x-squared, which is x times x, and here we have minus 4x, which is minus 4 times x.
This means that the variable x is in both of the terms, and we start by writing this down.
So x is one of the factors, but it’s not in our list of answers to choose from. So we have to find another factor, like over here when we created factor pairs.
Therefore we put a pair of brackets next to the x and inside the brackets we need to write terms that will take us back to the origin expression when they are multiplied by the x we’ve written here.
So if we put an x here, the brackets tell us that this means x times x, which gives x-squared.
And if we write minus 4 here, the brackets tell us that it also means x times minus 4 which gives us the minus 4x we started with.
So what we’ve created here on the left is the factorised version of what we started with.
And so if we remind ourselves of the factor pairs we had here for the number 6, what we’ve done is create the algebra version of a factor pair, where one of the factors is x and the other is x minus 4.
This is because when x is multiplied by x minus 4 we get back to the original expression, in the similar way to what we had here.
So when we look at the four possible answers, we find that the answer to this question is x minus 4.
I hope this has helped you answer this type of higher level GCSE exam question.
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As always, I’ll do my best to get back to you and wish you all the best with your studies.
Bye for now.
17 сен 2024
