Common factors: Noobie question!!

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)

with the answer being

(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!!

Original post by Desade777

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)

with the answer being

(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 :smile:

x(x-2)+3(2-x)=x(x-2)-3(x-2)=(x-2)(x-3)

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

a=x-2

then you'd have

xa-3a

I'm sure you're confident on how to factor the a out of here.

Reply 2

navip

6

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