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8.1 – Monomials & Factoring

8.1 – Monomials & Factoring. Factoring Factoring – opposite of simplifying!

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8.1 – Monomials & Factoring

Factoring

Factoring – opposite of simplifying!

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 105.

15 · 7

Factoring – opposite of simplifying!

Ex. Simplify 3(5)(7).

15(7)

105

Ex. Factor 105.

15 · 7

3 · 5 · 7

2 Types of Numbers:

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 itselfComposite – a whole number, greater than 1, that has more than two factors

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P C

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P C P

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P C P C

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P C P C C

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P C P C C 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.

13 36 23 14 15 19

P C P C C P

*prime factorization

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

Ex. 1 Classify each as prime or composite.13 36 23 14 15 19P C P C C P

*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

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

9 · 10

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

9 · 10

3·3

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

9 · 10

3·3 2·5

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

9 · 10

3·3·2·5

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

9 · 10

3·3·2·5

b. -140

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

9 · 10

3·3·2·5

b. -140

-1 · 140

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

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

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 -1·22·5·7

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 -1·22·5·7

*greatest common factor (GCF)

*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 2·2·2·2 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 2·2 = 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 2·2·2·2 2·2 = 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 2·2·2·2 2·2 = 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 2·2·2·2 2·2 = 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 2·2·2·2 2·2 = 4

b. 29 & 38 1·29 2·19 N/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 2·2·2·2 2·2 = 4

b. 29 & 38 1·29 2·19 N/A

c. 36x2y & 56xy2

*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 2·2 = 4

b. 29 & 38 1·29 2·19 N/A

c. 36x2y & 56xy2

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 2·2·2·2 2·2 = 4

b. 29 & 38 1·29 2·19 N/A

c. 36x2y & 56xy2

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 2·2·2·2 2·2 = 4

b. 29 & 38 1·29 2·19 N/A

c. 36x2y & 56xy2

2·2·3·3·x·x·y 2·2·2·7·x·y·y 2·2·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 2·2·2·2 2·2 = 4

b. 29 & 38 1·29 2·19 N/A

c. 36x2y & 56xy2

2·2·3·3·x·x·y 2·2·2·7·x·y·y 2·2·x·y = 4xy