Factoring Simple Algebraic Expressions

Factoring Simple Algebraic Expressions

MR. BOWIE

Variable factors

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.

Factors of terms

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: 

 $2\ \times3x\$  
 $3\ \times\ 2x$  
 $2\ \times\ 3\ \times\ x$   
Therefore, factors of 6x = 2, 3, 2x, 3x, x. 

Highest Common Factor (HCF)

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.

Example 2

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

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

 $21y\ =\ 1,\ 3,\ 7,\ 21,\ y,\ 3y,\ 7y,\ 21y$  
 $9y^2\ =\ 1,\ 3,\ 9,\ y,\ y^2,\ 3y,\ 9y$  

 $Therefore,\ the\ HCF\ of\ 21y\ and\ 9y^2\ is\ 3y.$  

Multiple Select

List the common factors of 16x

• 1, 2, 4, 8, 16

• 1, 2, x, 8, 16, 4

• 1, 2, 4, 8, 16, x, 2x, 4x, 8x, 16x

• x, 2x, 4x, 8x, 16x

Multiple Choice

Find the HCF of 12h and 16h

• 2h

• 4h

• 6h

• 8h

Multiple Choice

How many factors does the term 7m have?

• 1

• 2

• 3

• 4

Multiple Choice

1,2,3, b, 2b and 3b are the factors of

• 6b

• 6

• 3b

• 3b + 2b

Multiple Choice

 $What\ is\ the\ HCF\ of\ 40p\ and\ 60p^2\ \ ?$   

• 10p

• 20p

• 30p

•  $20p^2$  
  

Multiple Choice

 $What\ is\ the\ HCF\ of\ 8x^2\ and\ 24$  

• 2

• 4

• 6

• 8

Factoring algebraic expressions

factoring is the act of finding the numbers or expressions that multiply together to make a given number or equation. Factoring is a useful skill to learn for the purpose of solving basic algebra problems. Factoring can be used to simplify algebraic expressions to make solving simpler.

Example 1

Factorize the expression

 $2x\ +\ 4$  

Solution
 $Step\ 1.\ divide\ both\ terms\ \left(2x\ \&\ 4\right)\ by\ 2\ which\ is\ their\ HCF\$   $2x\ \div2\ \ +\ 4\ \div\ 2$  
 $Step\ 2.\ keep\ the\ 2\ outside\ of\ a\ bracket\ the\ contains\ the\ quotients\$   $2\left(x\ +\ 2\right)$  
 $Therefore,\ when\ 2x\ +\ 4\ is\ factorize\ the\ solution\ is\ 2\left(x\ +\ 2\right).$  

Example 2

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

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

Multiple Choice

 $Factorize\ \ \ 2p\ +\ p^2.$  

•  $2\left(1\ +\ p\right)$  

•  $p\left(2\ +\ p\right)$  

•  $p^2\left(2+\ p\right)$  

Multiple Select

 $Factorize\ \ \ 9x^2\ -\ 3x^3$  

•  $9x\left(x\ -\ 3x^2\right)$  

•  $3x\left(3x\ -\ x^3\right)$  

•  $3x^2\left(3\ -\ x\right)$  

•  $3x^2\left(3x\right)$  

Poll

How was your experience learning about factoring algebraic expressions?

• It was fun

• I learned a lot

• It was confusing

• Still don't get it

• I understand it