1. Factoring Using the Distributive Property
9.2
Factoring Using the Distributive Property

2. Greatest Common Factor (GCF)/Distributive Property
Look for the largest common number and/or variables in each term
Divide each term by the common terms

3. Use the Distributive Property to factor .
First, find the CGF of 15x and .
Factor each number.
Circle the common prime factors.
GFC:
Write each term as the product of the GCF and its remaining factors. Then use the Distributive Property to factor out the GCF.
Rewrite each term using the GCF.
Simplify remaining factors.
Distributive Property
Example 2-1a

4. Answer: The completely factored form of is
Example 2-1a

5. Use the Distributive Property to factor .
Factor each number.
Circle the common prime factors.
GFC: or
Rewrite each term using the GCF.
Distributive Property
Answer: The factored form of is
Example 2-1a

6. Use the Distributive Property to factor each polynomial. a.
Answer:
Answer:
Example 2-1b

7. Grouping Steps Arrange terms in descending order
Separate into groups of 2 in ()
Factor the GCF from each group
Factor an additional (-1) if necessary
The terms in () must match
Combine the two GCF into a binomial in () and place it next to the other binomial

8. Grouping Example

9. Group terms with common factors.
Factor the GCF from each grouping.
Answer:
Distributive Property
Example 2-2a

10. Factor
Answer:
Example 2-2b

11. Group terms with common factors.
Factor GCF from each grouping.
Answer:
Distributive Property
Example 2-3a

12. Factor
Answer:
Example 2-3b

13. Solve Then check the solutions.
If , then according to the Zero Product Property either or
Original equation or
Set each factor equal to zero.
Solve each equation.
Answer: The solution set is
Example 2-4a

14. Check Substitute 2 and for x in the original equation.
Example 2-4a

15. Solve Then check the solutions.
Answer: {3, –2}
Example 2-4b

16. Solve Then check the solutions.
Write the equation so that it is of the form
Original equation
Subtract from each side.
Factor the GCF of 4y and which is 4y.
Zero Product Property or
Solve each equation.
Example 2-5a

17. Answer: The solution set is Check by substituting
0 and for y in the original equation.
Example 2-5a

18. Solve
Answer:
Example 2-5b

19. Practice Problems
Page 484 Problems 4-15, 16-39, (odd)

20. Practice Problems (Day 2)
Page 484 Problems 4-15, 16-39, (even)