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Warm-Up Exercises 1.) Write the prime factorization for 36 2.) What are some factors of 36?

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Section 8.1 Section 8.2 Section 8.3 Section 8.4 Section 8.5 Section 8.6

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Factors and Greatest Common Factors

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Goals Students will be able to write the prime factorization of numbers. Students will be able to find the GCF of monomials.

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Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor.

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Communicate Effectively By using technology to receive, process and send information By reading and writing at an appropriate grade level Demonstrate effective oral and listening skills Learn to use English to express themselves clearly

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Examples Write out the prime factorization of 60. Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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Definition Factors that are shared by two or more whole numbers are called common factors. The greatest of these common factors is called the greatest common factor (GCF). Examples: Factors of 12: 1,2,3,4,6,12 Factors of 32: 1,2,4,8,16,32 Common Factors: 1,2,4 Largest Common Factor = 4 = GCF Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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Examples Find the GCF of 24 and 60 Method 1: List the factors Factors of 24: 1,2,3,4,6,8,12,24 Factors of 60: 1,2,3,4,5,6,10,12,15,20,30,60 Largest common factor = 12 = GCF Method 2: Use Prime Factorizations 24 = 2 2 2 3 60 = 2 2 3 5 Factors they have in common: 2,2 GCF = 2 2 = 4 Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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Examples Find the GCF of 12 and 24 by listing out the factors Find the GCF of 100 and 60 by using the prime Factorizations. Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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Finding the GCF of Monomials Find the GCF of 3x 2 and 6x 2. Prime factorization of 3x 2 : 3 x x Prime factorization of 6x 2 : 2 3 x x Common Factors: 3 x x = 3x 2 Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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Student Example Find the GCF of 8x 2 y and 20xy 2. Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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Homework Section 8.1 Pg. 481 #’s 2-22 evens Goals -Students will be able to write the prime factorization of numbers. -Students will be able to find the GCF of monomials. Standards Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor. ESLR: Communicate Effectively

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