8.1 – Monomials & Factoring

Factoring

Factoring – opposite of simplifying!

Ex. Simplify 3(5)(7).

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

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

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

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

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

2 Types of Numbers:

Prime

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

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

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

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

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 P

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 PC

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 PCP

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 PCPC

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 PCPCC

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 PCPCCP

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 PCPCCP *prime factorization

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 PCPCCP *prime factorization – when a whole number is expressed as the product of factors that are all prime numbers

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

9 · 10

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

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

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

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

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

Ex. 2 Find the prime factorization of the following:a · 10 3·3·2·5 b · · 14 · · 2·7 · 2·5

Ex. 2 Find the prime factorization of the following:a · 10 3·3·2·5 b · · 14 · · 2·7 · 2·5

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

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

*greatest common factor (GCF)

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

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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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

*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