Factoring Simple Algebraic Expressions

You have been exposed to whole number factors throughout your Mathematical development. Today we will be embarking on a journey with a new type of factor called "Variable Factor". It is simple a variable or term that can be evenly divided into another variable or term. Exactly the same as whole number factors.

Just like ordinary numbers, algebraic terms have factors. We use these factors to factorize and simplify algebraic expressions.

Example
List the factors of 6x

Pairs of factors of 6x are: 

When factoring algebraic expressions it is less time consuming to factorize using the highest common factors of each terms.

Example 1

List the HCF of 10x and 15

common factors of 10x and 15 are:

10x = 1, 2, 5, 10, x, 2x, 5x, 10x

15 = 1, 3, 5, 15

Therefore, the HCF of 10x and 15 is 5.

 $Find\ the\ HCF\ of\ 21y\ and\ 9y^2$  

 $Common\ factors\ of\ 21y\ and\ 9y^2\ are:$  

Factorize the expression

 $Factorize\ 4x\ -\ 20x^2$  
Solution
 $\ 4x\left(\frac{4x}{4x}\ -\ \frac{20x^2}{4x}\right)$  
 $4x\left(1\ -\ 5x\right)$  

 $Therefore,\ 4x\ -\ 20x^2\ =\ 4x\left(1\ -\ 5x\right).$