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Published byMilton Hood Modified over 8 years ago

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Objectives The student will be able to: 7A: Find the prime factorization of a number, the greatest common factor (GCF) for a set of monomials and polynomials.

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

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1) Find the prime factorization of 84. 84=4 21 =2 2 3 7 2) Find the prime factorization of 45a 2 b 3 = 9 5 a a b b b =3 3 5 a a b b b = 3 2 5 a a b b b Write the variables without exponents.

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The Greatest Common Factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. 4) Find the GCF of 42 and 60. Write the prime factorization of each number.

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4) 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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5) 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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Review: What is the GCF of 25a 2 and 15a? 5a Let’s go one step further… 1) FACTOR 25a 2 + 15a. Find the GCF and divide each term 25a 2 + 15a = 5a( ___ + ___ ) Check your answer by distributing. 5a3

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2) Factor 18x 2 - 12x 3. Find the GCF 6x 2 Divide each term by the GCF 18x 2 - 12x 3 = 6x 2 ( ___ - ___ ) Check your answer by distributing. 32x

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3) Factor 28a 2 b + 56abc 2. GCF = 28ab Divide each term by the GCF 28a 2 b + 56abc 2 = 28ab ( ___ + ___ ) Check your answer by distributing. 28ab(a + 2c 2 ) a2c 2

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5) Factor 28a 2 + 21b - 35b 2 c 2 GCF = 7 Divide each term by the GCF 28a 2 + 21b - 35b 2 c 2 = 7 ( ___ + ___ - ____ ) Check your answer by distributing. 7(4a 2 + 3b – 5b 2 c 2 ) 4a 2 5b 2 c 2 3b

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