The following steps will be useful to factor linear expressions.
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.
Example 1 :
Factor :
4x + 8
Solution :
Find the largest common divisors for 4x and 8.
The largest common divisor for 4x and 8 is 4.
Divide 4x and 8 by 4
4x/4 = x
8/4 = 2
Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.
4(x + 2)
Example 2 :
Factor :
16a + 64b - 4c
Solution :
Find the largest common divisors for 16a, 64b and 4c.
The largest common divisor for 16a, 64b and 4c is 4.
Divide 16a, 64b and 4c by 4
16a/4 = 4a
64b/4 = 16b
4c/4 = c
Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.
4(4a + 16b - c)
Example 3 :
Factor :
36x - 16
Solution :
Find the largest common divisors for 36x and 16.
The largest common divisor for 36x and 16 is 4.
Divide 36x and - 16 by 4.
36x/4 = 9x
-16/4 = -4
Write the quotients 9x and -4 inside the parenthesis and multiply by the largest common divisor 4.
4(9x - 4)
Example 4 :
Factor :
35 + 21a
Solution :
Find the largest common divisors for 35 and 21a.
The largest common divisor for 35 and 21a is 7.
Divide each term by 7
35/7 = 5
21a/7 = 3a
Write the quotients 5 and 3a inside the parenthesis and multiply by the largest common divisor 7.
7(5 + 3a)
So,
35 + 21a = 7(5 + 3a)
Example 5 :
Factor :
4a - 8b + 5ax - 10bx
Solution :
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.
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
So,
= 4(a - 2b) + 5x (a - 2b)
= (a - 2b) (4 + 5x)
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