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8.1 – Monomials & Factoring

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Factoring

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Factoring – opposite of simplifying!

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Ex. Simplify 3(5)(7).

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Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7)

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Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105

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Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105 Ex. Factor 105.

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Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105 Ex. Factor 105. 15 · 7

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Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105 Ex. Factor 105. 15 · 7 3 · 5 · 7

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2 Types of Numbers:

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Prime

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 P

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PC

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PCP

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PCPC

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PCPCC

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PCPCCP

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PCPCCP *prime factorization

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2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 133623141519 PCPCCP *prime factorization – when a whole number is expressed as the product of factors that are all prime numbers

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Ex. 2 Find the prime factorization of the following:a. 90

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9 · 10

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3 2·5

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3·2·5

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3·2·5 b. -140

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5

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Ex. 2 Find the prime factorization of the following:a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5

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Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5 -1·2 2 ·5·7

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Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5 -1·2 2 ·5·7

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*greatest common factor (GCF)

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- the greatest number that is a factor of all numbers in the expression

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·x·y·y

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·x·y·y

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·x·y·y2·2·x·y

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*greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·x·y·y2·2·x·y = 4xy

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Prime and Composite Numbers A prime number is a natural number greater than 1 whose only factors are 1 and itself. The first few prime numbers are 2,

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