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Common factors: Noobie question!! watch

1. There's a question in the AQA C1 book at the end of Chapter 1

Take out the common factor of
x(x-2) + 3(2-x)

(x-2) (x-3)

however no explanation is given. I can see how the two are related (x^2 - 5x + 6) but am having a brain block and missing out how to work it out without clumsily back tracking from the solution. Can someone please give me dummies explanation.....sorry about the simplicity of the question it's been MANY years since I studied maths!!
There's a question in the AQA C1 book at the end of Chapter 1

Take out the common factor of
x(x-2) + 3(2-x)

(x-2) (x-3)

however no explanation is given. I can see how the two are related (x^2 - 5x + 6) but am having a brain block and missing out how to work it out without clumsily back tracking from the solution. Can someone please give me dummies explanation.....sorry about the simplicity of the question it's been MANY years since I studied maths!!
Better get used to these fast then

The last step is simply factoring out the common factor of (x-2). If you don't know what happens in the last step, let then you'd have I'm sure you're confident on how to factor the a out of here.
3. Just adding to the previous answer, the key step is to flip the sign of (2-x) to (-2+x) which is (x-2) and negating the term. That way you get a common factor between the two terms without changing the value
4. (Original post by RDKGames)
Better get used to these fast then

The last step is simply factoring out the common factor of (x-2). If you don't know what happens in the last step, let then you'd have I'm sure you're confident on how to factor the a out of here.
Thank you! It's going to take a while to get back in the swing....it's been 30 years after all!!

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