8.1 – monomials & factoring
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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) - PowerPoint PPT PresentationTRANSCRIPT
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