Factorisation

[Josh3000]

Hi,

The task is to factorise the following statement:

6x - 3x^2

I can get 3(2x - x^2)

An answer I have been given is: 3x(2 - x) ... please can someone explain as simply as possible how you get to this answer. I cannot understand how you get this at all.

Thanks so much.

Josh

 

[Deleted member 4993]

Hi,

The task is to factorise the following statement:

6x - 3x^2

I can get 3(2x - x^2)

An answer I have been given is: 3x(2 - x) ... please can someone explain as simply as possible how you get to this answer. I cannot understand how you get this at all. Thanks so much. Josh

You have taken the correct steps. You have factored out 3 from the expression. You are almost there! Just one more step.

Look at the expression inside the parentheses (). There is a common factor there. This common factor is NOT a given number (like 3 in the previous step). Do you recognize that common factor?

 

[JeffM]

The fundamental idea in algebra notation is that a given letter stands for a number that we do not yet know. So x is just a number (even though we do not know its value yet), and it can be factored out just like 3 if it is a common factor.

So what then does [MATH]x^2[/MATH] stand for? It stands for [MATH]x * x[/MATH].

[MATH]6x - 3x^2 = 3(2x - x^2) = 3\{(2 * x) - (x * x)\} = 3\{x(2 - x)\} = 3x(2 - x).[/MATH]
Once you recognize that [MATH]x^2 \equiv x * x[/MATH], you should see that it has a common factor
with 2x = 2 * x, namely both products have x as the second factor.