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MJ2A Ch 4.3 – Prime Factorization

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Bellwork Evaluate each expression 1. 3(b – 1) 4 where b = 4 2. 3(3c + 7) 2 where c = -3

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Assignment Review Text p. 155 – 156 # 12 – 40 Do not do # 24 – 27!

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Before we begin… Please take out your notebooks and get ready to work… In today’s lesson we will continue to work with factors…specifically we will look at the prime factorization of composite numbers and monomials… Please raise your hand if you can tell me what a prime number is…. …a composite number…

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Objective 4.3 Students will write the prime factorization of composite numbers and monomials

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Vocabulary Prime Number – a whole number that has only 2 factors…one and itself… Let’s make a list of the prime numbers from 1 to 31… Basically…you should be able to recognize these numbers as prime numbers…this will help when doing prime factorization of composite numbers….

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Vocabulary Composite number – a whole number with more than two factors Note: The numbers 0 (zero) and 1 (one) are neither prime nor composite numbers!

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Prime Factorization When doing the prime factorization of a number the goal is to get down to the prime numbers so that when they are multiplied they will give you the composite number There are a number of methods to get to the prime factorization of a number. The 3 that we will look at today are: Listing the factors Factor Tree Cake Method

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Listing the Factors One way to do prime factorization is to list the factors. Start with the first and last and then work backwards. Example (demonstrate on board) 12 The listing method works well if you are doing small numbers and/or are very familiar with the multiplication tables…

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Factor Tree Another method to do the prime factorization is the factor tree. Let’s look at an example…

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Prime Factorization of 24 24 6 x 4 2 x 3 x 2 x 2 Prime factorization = 2 3 x 3 Choose any two factors of 24 Factor each number until you get to the prime numbers Write ALL of the prime numbers on the same line!

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Cake Method You can also use the cake method to factor the number 24. Divide each number by a prime number until your result is 1 Let’s look at an example…

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Cake Method 224 212 263 1 Prime Factorization = 2 x 2 x 2 x 3 = 2 3 x 3 Prime Factors of 24

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Comments At this point you get to choose….when doing the prime factorization of a number you get to choose which method works best for you….sometimes the listing method is the most efficient…however, if you have a big number the cake method is probably a better choice…when using the factor tree make sure that you list all the prime numbers on the bottom row…

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Your Turn In the notes section of your notebook write the number and then choose any method to do the prime factorization of the number. 1. 105 2. 84 3. 50

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Factoring Monomials Writing the prime factorization of a monomial is no different than doing the prime factorization of a number. The goal is to get to the prime numbers… Let’s look at an example…

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Factoring 4c 2 Using a factor tree: 4c 2 2 x 2 x c x c

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Your Turn In the notes section of your notebook write each of the monomials and then factor using any method. 1. 5a 2 b 2. -70xyz 3. 64n 3

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Summary In the notes section of your notebook summarize the key concepts covered in today’s lesson Today we discussed Prime Factorization using listing, factor tree & cake methods Prime Factorization of monomials

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Assignment Text p. 162 # 25 – 40 This assignment is due tomorrow I do not accept answers only! You must show how you got the prime factorization…use any method…

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