MJ2A

Ch 4.3 – Prime Factorization

Bellwork

Evaluate each expression

1. 3(b – 1)4 where b = 42. 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 factorsNote: 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 numberThere 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 factorsFactor TreeCake 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) 12The 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

24

6 x 4

2 x 3 x 2 x 2Prime factorization = 23 x 3

Choose any two factors of

24

Factor each number until

you get to the prime numbers

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 1Let’s look at an example…

Cake Method

2 24 2 12

2 63 3

1Prime Factorization = 2 x 2 x 2 x 3 = 23 x 3

Prime Factors

of 24

Prime Factors

of 24

Prime Factors

of 24

Prime Factors

of 24

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

In the notes section of your notebook write the number and then choose any method to do the prime factorization of the number.

1. 1052. 843. 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 4c2

Using a factor tree:4c2

2 x 2 x c x c

Your Turn

In the notes section of your notebook write each of the monomials and then factor using any method.

1. 5a2b2. -70xyz3. 64n3

Summary

In the notes section of your notebook summarize the key concepts covered in today’s lessonToday we discussed

Prime Factorization using listing, factor tree & cake methodsPrime Factorization of monomials

Assignment

Text p. 162 # 25 – 40This assignment is due tomorrowI do not accept answers only!You must show how you got the prime factorization…use any method…