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LESSON ESSENTIAL QUESTION WHAT IS A GREATEST COMMON FACTOR (GCF)? HOW DO YOU USE GCF TO FACTOR FUNCTIONS? Greatest Common Factor

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JOURNAL Explain how to reduce the fraction 9/12. Don’t just do it, explain in words HOW to do reduce a fraction.

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Reducing a fraction Reduce the fraction 9/12 into simplest form Did you know that since elementary school, you have been using Greatest Common Factors when you reduce fractions We are going to take our knowledge of GCF to another level today

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What is a factor? Factors are the numbers you multiply together to get another number List all the factors of 12 1, 12, 2, 6, 3, 4 List all the factors of 16 1, 16, 2, 8, 4

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What is GCF? What is a Greatest Common Factor (GCF)? The highest number that divides exactly into 2 or more numbers. Now that we know what the factors of 12 and 16 are, let’s take a look at the GCF of 12 and 16. What should we be looking for?

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GCF of 12 and 16 Step 1: Find all the factors of each number Step 2: Circle the common factors Step 3: Choose the greatest number circled of the common factors Factors of 12: 1, 12, 2, 6, 3, 4 Factors of 16: 1, 16, 2, 8, 4 4 is the Greatest Common Factor (GCF)

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Factors of 60 Factors of 96 160 230 320 415 512 610 196 2 48 332 424 6 16 8 12 What is the GCF of 60 & 96?

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SKETCH’S WORLD GCF GAME Help Sketch stay away from the eraser by finding the GCF http://www.fun4thebrain.com/beyondfacts/gcfsketc h.html http://www.fun4thebrain.com/beyondfacts/gcfsketc h.html

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2 ways to GCF There are 2 ways to finding the Greatest Common Factor…..We have explored one of the ways! 1. Listing all factors and picking the largest one 2. Prime factorization Now, we need to discuss what a “prime” number is…..

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What is a prime number? A prime number is a number that can only be divided by only 1 and itself. A composite number is a number greater than one that is not prime. It has factors. Prime or composite? 37 prime 51 composite

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Prime or Composite? 1. Prime 2. Composite 3. Both 4. Neither 89

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Find the prime factorization of 84. 84=4 21 =2 2 3 7

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What is the prime factorization of 48? 1. 3 16 2. 3 4 4 3. 2 2 3 4 4. 2 2 2 2 3

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Factorization of 60 Factorization of 96 Prime Factorization of 60 & 96

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Find the GCF of 42 and 60. What prime factors do the numbers have in common? Multiply those numbers. The GCF is 2 3 = 6 6 is the largest number that can go into 42 and 60! 42 =2 3 7 60=2 2 3 5

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You choose: Find the GCF of 24 & 48

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Fruit Shoot Game Find the Greatest Common Factor game http://www.sheppardsoftware.com/mathgames/frac tions/GreatestCommonFactor.htm http://www.sheppardsoftware.com/mathgames/frac tions/GreatestCommonFactor.htm

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JOURNAL: Let’s practice some more Choose a method and find the GCF of the following pairs of numbers: Check your answer with your shoulder buddy. a) 10 and 50 b)40 and 95 c)18 and 63 d)32 and 92

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What is the GCF of 48 and 64? 1. 2 2. 4 3. 8 4. 16

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Finding GCF: Extra practice (if needed) http://www.mathopolis.com/questions/q.php?id=9 20&site=1&ref=/greatest-common- factor.html&qs=920_921_1382_1383_3548_3549_ 3550_3551 http://www.mathopolis.com/questions/q.php?id=9 20&site=1&ref=/greatest-common- factor.html&qs=920_921_1382_1383_3548_3549_ 3550_3551

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What do you think…. How do you find the GCF of variables?!?!

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45A 2 B 3 = 9 5 A A B B B = 3 3 5 A A B B B WRITE THE VARIABLES WITHOUT EXPONENTS. Find the prime factorization of 45a 2 b 3

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10cd 2 25c 3 d 2 2*5*c*d*d 5*5*c*c*c*d*d GCF Monomials http://www.khanacademy.org/math/algebra/multiplying-factoring- expression/multiplying%20monomials/v/monomial-greatest-common-factor

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Find the GCF of 40a 2 b and 48ab 4. 40a 2 b = 2 2 2 5 a a b 48ab 4 = 2 2 2 2 3 a b b b b What do they have in common? Multiply the factors together. GCF = 8ab

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You Try…. Find the GCF of 8a 2 b and 18a 2 b 2 c The GCF is 2a 2 b

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HOMEWORK COMPLETE THE GCF WORKSHEET FOR HOMEWORK TONIGHT

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LESSON ESSENTIAL QUESTION: HOW DO YOU USE GCF TO FACTOR POLYNOMIALS? Factoring a Monomial from a polynomial

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JOURNAL: WARMUP Find the GCF of 10x 2 y 3 and 15xy 2

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What more can we do with GCF? Now, that we have mastered how to GCF monomials…… We are going to GCF polynomials

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We have seen that we use multiplication to get 4x 2 (2x + 1) = 8x 3 + 4x 2 What if we start with 8x 3 + 4x 2 and want to get to 4x 2 (2x + 1) ? How do we do that??

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Factoring Polynomials Factoring a polynomial means finding an equivalent expression that is a product. Let’s start exploring into bigger polynomials and see what we can figure out

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Finding Common Factors http://regentsprep.org/Regents/math/ALGEBRA/A V6/Lfaccom.htm http://regentsprep.org/Regents/math/ALGEBRA/A V6/Lfaccom.htm

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Factoring a Monomial from a polynomial Factor 12x 2 - 9x Think…what is the GCF???? 3x is the GCF The GCF always goes on the outside of the parenthesis. The “leftovers” go in the parenthesis Answer: 3x(4x - 3)

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Factoring a Monomial from a Polynomial Factor 15x 2 y 3 + 10xy 2 The largest integer that will divide into 15 and 10 is _____ The largest power of x in both terms is ________ The largest power of y in both terms is ________ The GCF is _________Answer:________________

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Quick Check: GCF Binomials 4x + 4y 4x – 4y 6x – 18y 4a + 36b 4ab + 10bc 4( x + y) 4( x - y) 6( x - 3y) 4( a + 9b) 2b( 2a + 5c)

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Quick Check: GCF Binomials 3x 2 + 9x 16x + 48x 2 10x - 8x 2 12a 2 b + 32ab 25a 2 t + 100at 2 3x( x + 3) 16x( 1 +3x) 2x( 5 – 4x) 4ab(3a + 8 25at(a + 4t)

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CLASS WORK Complete the Factoring Binomials worksheet

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Practice with Factoring http://regentsprep.org/Regents/math/ALGEBRA/A V6/PracFact4.htm http://regentsprep.org/Regents/math/ALGEBRA/A V6/PracFact4.htm

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Factoring a Monomial from a polynomial Factor 9x 4 + 18x 3 + 6x 2 Think…what is the GCF???? 3x 2 is the GCF Answer: 3x 2 (3x 2 + 6x + 2)

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Factoring GCF & Trinomials http://www.themathlab.com/Algebra/factoring/grt mono1.htm#answers http://www.themathlab.com/Algebra/factoring/grt mono1.htm#answers

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GCF Trinomials

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GCF QUIZ http://www.softschools.com/quizzes/algebra/findin g_the_greatest_common_factor_gcf_of_two_or_m ore_monomials/quiz5018.html http://www.softschools.com/quizzes/algebra/findin g_the_greatest_common_factor_gcf_of_two_or_m ore_monomials/quiz5018.html

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