8.1 Monomials and Factoring

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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.
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A prime number is a

• number that can only be divided by 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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Ex 1 Prime or Composite?89

1. Prime
2. Composite
3. Both
4. Neither

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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

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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.

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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.

• Ex 5) Find the GCF of 42 and 60.
• Write the prime factorization of each number.

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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!

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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

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Ex 7) What is the GCF of 48 and 64?

1. 2
2. 4
3. 8
4. 16

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