Lesson BASICS - Factoring

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This Lesson (BASICS - Factoring) was created by by longjonsilver(2297) About Me : View Source, Show
About longjonsilver: I have a new job in September, teaching
Introduction
Factorisation is the process of converting a single or many terms into 2 (or more) terms that are MULTIPLIED together.

This is where the name factorisation comes from --> in 2*3, the 2 and the 3 are called factors because they are multiplied together.

So, to factorise means "to write as terms multiplied together"



Examples
Factorise 12 --> answer is 12*1 or 4*3 or 6*2 or any other combination eg 2.5*4.8.

However, when asked to factorise, it is assumed it means to find integer factors

Example
Factorise 3xy --> this is already factorised, since it is 3*x*y.

Example
Factorise 4x + 6y --> OK, we have 2 terms. Is there anything common to both of them?

Well, lets look at the 2 terms as 2*2*x + 2*3*y. OK, what about now? What is common to both? Answer is a 2. This is going to be one of our factors.

so we have 2 times "WHAT" gives 2*2*x + 2*3*y?
how about 2 times (2*x + 3*y)? Check this by multiplying the bracket by the 2...we get the original.

so, the answer here is 2(2x+3y)

If you can understand that question, you can do any factorisation question of a set of terms like this. There are slightly more intricate skills involved in factorising quadratics for example, but they are still essentially based upon what i have shown here in these first 3 examples.

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Further Examples
Factorise 4x%5E3+-+12x%5E2 --> the answer is 4x%5E2%28x-3%29

Where is this gotten? Well, 4x%5E3+-+12x%5E2 is 4%2Ax%2Ax%2Ax+-+4%2A3%2Ax%2Ax...what is THE MOST common to both terms? well both have a 4 and x and x... so lets take this out of both terms:

We get 4*x*x times "WHAT"? is 4*x*x*x - 4*3*x*x ?
answer is 4*x*x times (x - 3) is 4*x*x*x - 4*3*x*x
--> 4x%5E2%2A%28x-3%29 is 4x%5E3+-+12x%5E2

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Summary
The skill of factoring starts with simple examples like these here. Factorisation is a very important algebra skill to acquire since it is used in solving Quadratic equations and in simplifying algebraic expressions.

I shall cover these topics in later Lessons.
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