Chapter 5 Factoring
5.2
Finding the Greatest Common Factor of Polynomials
In a multiplication problem, the numbers multiplied together are called factors. The answer to a
multiplication problem is a called the product.
In the multiplication problem 6 × 4 = 24, 6 and 4 are factors and 24 is the product.
If we reverse the problem, 24 = 6 × 4, we say we have factored 24 into 6 × 4.
In this chapter, we will factor polynomials.
Example 1:
Step 1:
Find the greatest common factor of 3|3 + 6| 2 .
Look at the whole numbers. The greatest common factor of 3 and 6 is 3.
Factor the 3 out of each term.
3 (| 3 + 2| 2 )
Step 2:
Look at the remaining terms, | 3 + 2| 2 . What are the common factors of each
term?
|3
2| 2
= |
=
× |
|
× |
# common factors = |2
× |
Step 3:
Factor 3 and | 2 out of each term: 3|2 (| + 2)
Check:
3| 2 (| + 2) = 3| 3 + 6| 2
Factor by finding the greatest common factor in each of the following.
1. 16{4 + 8{3
11. 2p3 + 8p4
2. 14| 3 + 2| 2
12. 10{4 5{3
3. 4e5 + 8e8
13. 4e4 2e3
4. 10d3 + 5d4
14. 8f2 + 4f
5. 3|3 + 6| 2
15. 20| 3 + 10| 5
6. 8{6 12{2
16. 6{2 4{5
7. 8|2 2|
17. 5d4 5d2
8. 5d3 5d2
18. 4e3 + 6e6
9. 4{3 + 6{2
19. 6|4 + 9| 2
10. 6e2 + 2e5
20. 2{3 + 4{
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