Lesson BASICS - Factoring
Algebra
->
Expressions
-> Lesson BASICS - Factoring
Log On
Algebra: Evaluation of expressions, parentheses
Section
Solvers
Solvers
Lessons
Lessons
Answers archive
Answers
Source code of 'BASICS - Factoring'
This Lesson (BASICS - Factoring)
was created by by
longjonsilver(2297)
:
View Source
,
Show
About longjonsilver
:
I have a new job in September, teaching
<b>Introduction</b> 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" <b>Examples</b> Factorise 12 --> answer is 12*1 or 4*3 or 6*2 or any other combination eg 2.5*4.8. <b>However, when asked to factorise, it is assumed it means to find integer factors</b> <b>Example</b> Factorise 3xy --> this is already factorised, since it is 3*x*y. <b>Example</b> 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. ----------------------------------------------------------------------------------- <b>Further Examples</b> Factorise {{{4x^3 - 12x^2}}} --> the answer is {{{4x^2(x-3)}}} Where is this gotten? Well, {{{4x^3 - 12x^2}}} is {{{4*x*x*x - 4*3*x*x}}}...what is <b>THE MOST</b> 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^2*(x-3)}}} is {{{4x^3 - 12x^2}}} ----------------------------------------------------------------------------------- <b>Summary</b> 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.
