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8.1 Monomials and Factoring

Learn how to find the prime factorization of monomials and determine the greatest common factor (GCF) for a set of monomials. Discover the difference between prime and composite numbers.

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8.1 Monomials and Factoring

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  1. 8.1 Monomials and Factoring Objective Students will be able to: 1. find the prime factorization of a monomial. 2. find the greatest common factor (GCF) for a set of monomials.

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

  3. Ex 1: Prime or Composite?89 • Prime • Composite • Both • Neither

  4. Ex 2) Find the prime factorization of 84. 84 = 4 • 21 = 2 • 2 • 3 • 7 = 22 • 3 • 7 Ex 3) Find the prime factorization of -210. -210 = -1 • 210 = -1 • 30 • 7 = -1 • 6 • 5 • 7 = -1 • 2 • 3 • 5 • 7

  5. Ex 4) Find the prime factorization of 45a2b3 45a2b3 = 9 • 5 • a • a • b • b • b = 3 • 3 • 5 • a • a • b • b • b = 32 • 5 • a • a • b • b • b Write the variables without exponents.

  6. The Greatest Common Factor (GCF)of 2 or more numbers is the largest number that can divide into all of the numbers. Ex 5) Find the GCF of 42 and 60. Write the prime factorization of each number.

  7. Ex 5) Find the GCF of 42 and 60. • = 2 • 3 • 7 60 = 2 • 2 • 3 • 5 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!

  8. Ex 6) Find the GCF of 40a2b and 48ab4. 40a2b = 2 • 2 • 2 • 5 • a • a • b 48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b What do they have in common? Multiply the factors together. GCF = 8ab

  9. Ex 7) What is the GCF of 48 and 64? • 2 • 4 • 8 • 16

  10. 8.1 HW pg. 472 #10 – 21 all, 43 – 47 odd (15 problems)

  11. What is the prime factorization of 48? • 3  16 • 3  4  4 • 2  2  3  4 • 2  2  2  2  3

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