Section 8.5 Day 1 Using the Distributive Property

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Presentation transcript:

Section 8.5 Day 1 Using the Distributive Property Algebra 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(__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

(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

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