FACTORS OF  LINEAR EXPRESSIONS

About "Factors of linear expressions"

Factors of linear expressions :

Factoring (called "Factorising" in the UK) is the process of finding the factors. 

It is like "splitting" an expression into a multiplication of simpler expressions.

Factoring linear expressions - Steps

Step 1 : 

Find the largest common divisor for all the terms in the expression

Step 2 : 

Divide each term of the expression by the largest common divisor.

Step 3: 

Write the quotients inside the parenthesis. 

Step 4 : 

Write the largest common divisor and the parenthesis together using multiplication. 

Factors of linear expressions - Examples

Example 1 : 

Factor : 4x + 8

Solution : 

Step 1 : 

Find the largest common divisors for 4x and 8. 

The largest common divisor for 4x and 8 is 4. 

Step 2 :

Divide 4x and 8 by 4

4x / 4  =  x and 8 / 4  =  2

Step 3 :

Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.

4(x + 2)

Hence, 4x + 8  =  4(x + 2)

Example 2 : 

Factor : 16a + 64b - 4c

Solution : 

Step 1 : 

Find the largest common divisors for 16a, 64b and 4c. 

The largest common divisor for  16a, 64b and 4c is 4. 

Step 2 :

Divide 16a, 64b and 4c by 4 

16a / 4  =  4a, 64b / 4  =  16b and 4c / 4  =  c

Step 3 :

Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.

4(4a + 16b - c)

Hence, 16a + 64b - 4c  =  4(4a + 16b - c) 

Example 3 : 

Factor : 5x² - 15x

Solution : 

Step 1 : 

Find the largest common divisors for 5x² and 15x. 

The largest common divisor for 5x² and 15x is 5x. 

Step 2 :

Divide 5x² and 15x by 5x

5x² / 5x  =  x and 15x / 5x   =  3

Step 3 :

Write the quotients x and 3 inside the parenthesis and multiply by the largest common divisor 5x.

(5x)(x - 3)

Hence, 5x² + 15x  =  (5x)(x - 3)

Example 4 : 

Factor : 15y² - 9y +  6

Solution : 

Step 1 : 

Find the largest common divisors for 15y², - 9y and  6

The largest common divisor for 15y², - 9y and  6 is 3.

Step 2 :

Divide each term by 3

15y² / 3  =  5y², - 9y / 3   =  -3y, 6 / 3 = 2

Step 3 :

Write the quotients 5y², -3y and 2 inside the parenthesis and multiply by the largest common divisor 3.

3 (5y² -3y + 2)

Hence, 15y² - 9y +  6 =  3 (5y² -3y +2)

Example 5 : 

Factor : 4a - 8b + 5ax - 10bx

Solution : 

Step 1 :

Since we have four terms, we can group them into two terms

  =  4a - 8b + 5ax - 10bx

Common divisor for first two terms, that is 4a and 8b is 4

Common divisor for third and fourth terms, that is 5ax and 10bx is 5x.

Step 2 :

Divide first two terms by 4

4a/4  =  1a

- 8b/4  =  -2b

Divide third and fourth terms by 5x

5ax/5x  =  a

- 10bx/5x  =  -2b

Step 3 :

  =  4(a - 2b) + 5x (a - 2b)

=  (a - 2b) (4 + 5x)

After having gone through the stuff given above, we hope that the students would have understood "Factors of linear expressions". 

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