1. Section 8.5 Day 1 Using the Distributive Property
Algebra 1

2. Learning Targets
Find the greatest common factor between algebraic expressions
Factor a binomial
Factor a polynomial
Define and apply the Zero Product Property
Solve algebraic equations using factoring and the Zero Product Property

3. Greatest Common Factor (#): Level 1
Find the greatest common factor (GCF) of 24 and 12
GCF =12

4. Greatest Common Factor (#): Level 1
More Reps Find the GCF of 16 and 8 Answer: 8
More Weight
Find the GCF of 16 and 12
Answer: 4

5. Greatest Common Factor (#): Level 2
Find the greatest common factor (GCF) of 32 and 40 GCF =8

6. Greatest Common Factor (#): Level 2
More Reps Find the GCF of 105 and 45 Answer: 15
More Weight
Find the GCF of 85 and 102
Answer: 17

7. Greatest Common Factor (#): Procedure
Find the factors of each #
Factor Tree
List of Factors
Find all of the common factors
Multiply common factors together

8. Greatest Common Factor (#): Level 3
Find the greatest common factor (GCF) of 68, 102, & 238 GCF = 34

9. Greatest Common Factor (#): Level 3
More Reps Find the GCF of 24, 40, & 52 Answer: 4
More Weight
Find the GCF of 12, 36, 42, & 60
Answer: 6

10. Greatest Common Factor (Variables): Level 1
Find the greatest common factor (GCF) of 𝑥 6 and 𝑥 13 GCF = 𝑥 6

11. Greatest Common Factor (Variables): Level 1
More Reps Find the GCF of 𝑎 4 and 𝑎 2 Answer: 𝑎 2
More Weight
Find the GCF of 𝑥 2 𝑦 9 and 𝑥 5 𝑦 3
Answer: 𝑥 2 𝑦 3

12. Greatest Common Factor (Variables): Level 2
Find the greatest common factor (GCF) of 𝑥 𝑦 8 and 𝑥 7 𝑦 2 GCF = 𝑥 𝑦 2

13. Greatest Common Factor (Variables): Level 2
More Reps Find the GCF of 𝑎 8 𝑏 7 and 𝑎 Answer: 𝑎
More Weight
Find the GCF of 𝑤 5 𝑥 𝑦 12 and 𝑥 7 𝑦 2 𝑧 4
Answer: 𝑥 𝑦 2

14. Greatest Common Factor (Algebraic Expressions): EX 1
Find the GCF for 18 𝑥 2 and 24𝑥
GCF =6𝑥

15. Greatest Common Factor (Algebraic Expressions): EX 2
Find the GCF for 21 𝑦 3 and 30 𝑦 2
GCF =3 𝑦 2

16. Greatest Common Factor (Algebraic Expressions): EX 3
Find the GCF of 7 𝑢 2 𝑡 2 and 21𝑢 𝑡 2
GCF =7𝑢 𝑡 2

17. Greatest Common Factor (Algebraic Expressions): EX 4
Find the GCF of 36 𝑥 3 𝑦 and 35𝑥 𝑦 2
GCF = 𝑥∙𝑦=𝑥𝑦

18. GCF Puzzle Problem 1 Fill in the blanks knowing the final answer.
(5___)(___𝑥+6)=45 𝑥 2 +30𝑥
5𝑥 9𝑥+6 =45 𝑥 2 +30𝑥

19. (__𝑥__)(2__+__)=12𝑥 𝑦 5 +6 𝑥 7 𝑦 3
GCF Puzzle Problem 2
Fill in the blanks knowing the final answer.
(__𝑥__)(2__+__)=12𝑥 𝑦 5 +6 𝑥 7 𝑦 3
6𝑥 𝑦 3 2 𝑦 2 + 𝑥 6 =12𝑥 𝑦 5 +6 𝑥 7 𝑦 3

20. (2𝑥𝑦)(__+__+__)=6 𝑥 2 𝑦 7 −8 𝑥 8 𝑦 2 +2𝑥𝑦
GCF Puzzle Problem 3
Fill in the blanks knowing the final answer.
(2𝑥𝑦)(__+__+__)=6 𝑥 2 𝑦 7 −8 𝑥 8 𝑦 2 +2𝑥𝑦
2𝑥𝑦 3𝑥 𝑦 6 −4 𝑥 7 𝑦+1 =6 𝑥 2 𝑦 7 −8 𝑥 8 𝑦 2 +2𝑥𝑦

21. (__)(__+__+__)=3 𝑥 3 +27 𝑥 2 −9𝑥
GCF Puzzle Problem 4
Fill in the blanks knowing the final answer.
(__)(__+__+__)=3 𝑥 𝑥 2 −9𝑥
3𝑥 𝑥 2 +9𝑥−3 =3 𝑥 𝑥 2 −9𝑥