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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