Transcript MJ2A - Ch 4.3 Prime Factorization

MJ2A
Ch 4.3 – Prime Factorization
Bellwork
Evaluate each expression
1.
2.
3(b – 1)4 where b = 4
3(3c + 7)2 where c = -3
Assignment Review
Text p. 155 – 156 # 12 – 40
Do not do # 24 – 27!
Before we begin…
Please take out your notebooks and get ready to
work…
In today’s lesson we will continue to work with
factors…specifically we will look at the prime
factorization of composite numbers and
monomials…
Please raise your hand if you can tell me what a
prime number is….
…a composite number…
Objective 4.3
Students will write the prime factorization of
composite numbers and monomials
Vocabulary
Prime Number – a whole number that has only 2
factors…one and itself…
Let’s make a list of the prime numbers from 1 to
31…
Basically…you should be able to recognize
these numbers as prime numbers…this will help
when doing prime factorization of composite
numbers….
Vocabulary
Composite number – a whole number with more
than two factors
Note: The numbers 0 (zero) and 1 (one) are
neither prime nor composite numbers!
Prime Factorization
When doing the prime factorization of a number the
goal is to get down to the prime numbers so that when
they are multiplied they will give you the composite
number
There are a number of methods to get to the prime
factorization of a number.
The 3 that we will look at today are:
Listing the factors
Factor Tree
Cake Method
Listing the Factors
One way to do prime factorization is to list the
factors. Start with the first and last and then
work backwards.
Example (demonstrate on board) 12
The listing method works well if you are doing
small numbers and/or are very familiar with the
multiplication tables…
Factor Tree
Another method to do the prime factorization is
the factor tree.
Let’s look at an example…
Prime Factorization of 24
Factor each
number until
you get to
the prime
numbers
24
Choose any
two factors of
24
6x4
2x3x2x2
Prime factorization = 23 x 3
Write ALL of the
prime numbers
on the same
line!
Cake Method
You can also use the cake method to factor the
number 24. Divide each number by a prime
number until your result is 1
Let’s look at an example…
Cake Method
2 24
2 12
2
Prime
Factors
of 24
6
3
3
1
Prime Factorization = 2 x 2 x 2 x 3 = 23 x 3
Comments
At this point you get to choose….when doing the
prime factorization of a number you get to
choose which method works best for
you….sometimes the listing method is the most
efficient…however, if you have a big number the
cake method is probably a better choice…when
using the factor tree make sure that you list all
the prime numbers on the bottom row…
Your Turn
1.
2.
3.
In the notes section of your notebook write the
number and then choose any method to do the
prime factorization of the number.
105
84
50
Factoring Monomials
Writing the prime factorization of a monomial is
no different than doing the prime factorization of
a number.
The goal is to get to the prime numbers…
Let’s look at an example…
Factoring
2
4c
Using a factor tree:
4c2
2x2xcxc
Your Turn
1.
2.
3.
In the notes section of your notebook write
each of the monomials and then factor using
any method.
5a2b
-70xyz
64n3
Summary
In the notes section of your notebook summarize
the key concepts covered in today’s lesson
Today we discussed
Prime Factorization using listing, factor tree & cake
methods
Prime Factorization of monomials
Assignment
Text p. 162 # 25 – 40
This assignment is due tomorrow
I do not accept answers only!
You must show how you got the prime
factorization…use any method…