4.1 notes cardone.notebook
November 24, 2015
0
Nov 25­3:54 PM
1
4.1 notes cardone.notebook
November 24, 2015
Chapter 4 Factors, Fractions, and Exponents
Nov 26­9:59 AM
2
4.1 notes cardone.notebook
November 24, 2015
Section 4.1 Factors and Prime Factorization
Example 1
You are working on your school yearbook. Each page will have 24 student photos. The photos will be arranged in a rectangular display with the same number of photos in each row. How many ways can you arrange the photos so that there are no more than 10 photos in any row or column? [Hint: write 24 as a product of two whole numbers in all possible ways]
Nov 25­3:30 PM
3
4.1 notes cardone.notebook
November 24, 2015
Checkpoint
30
31
45
Nov 25­3:35 PM
4
4.1 notes cardone.notebook
November 24, 2015
prime number ­ a whole number that is greater than 1 and has exactly two whole number factors, 1 and itself
­ex: composite number ­ a whole number that is greater than 1 and has more than two whole number factors
­ex:
The number 1 is neither prime nor composite
Nov 25­3:37 PM
5
4.1 notes cardone.notebook
November 24, 2015
Examples of Prime and Composite Numbers
Number
Factors
Prime or Composite?
24
41
51
89
121
Nov 25­3:39 PM
6
4.1 notes cardone.notebook
November 24, 2015
prime factorization ­ when you write a number as a product of prime numbers
factor tree ­ a diagram used to write the prime factorization of a number
Nov 25­3:42 PM
7
4.1 notes cardone.notebook
November 24, 2015
Example 2
Write the prime factorization of 630.
Nov 25­3:45 PM
8
4.1 notes cardone.notebook
November 24, 2015
Checkpoint 59
32
Nov 25­3:46 PM
9
4.1 notes cardone.notebook
November 24, 2015
monomial ­ a number, a variable, or the product of a number and one or more variables raised to whole number powers
To factor a monomial, write the monomial as a product of prime numbers and variables with exponents of 1.
Monomials
Not Monomials
7x
7+x
25mn 2
25m-n 2
24y 3 z 2
24+y 3 +z 2
Nov 25­3:46 PM
10
4.1 notes cardone.notebook
November 24, 2015
Example 3
Factor the monomial 28xy3
Nov 25­3:49 PM
11
4.1 notes cardone.notebook
November 24, 2015
Checkpoint 15n3
6ab
Nov 25­3:53 PM
12
4.1 notes cardone.notebook
November 24, 2015
Nov 25­3:54 PM
13