FACTORIZING USINGCOMMON FACTORS

This presentation done by Zaheer Ismail

Key terms

Common Factor: A whole number that is a common factor of two or more nonzero whole numbers. i.e. 4 is a common factor for 12 and 20

Greatest Common Factor: The greatest of the common factors.

Factoring

Factoring is the process of finding all the factors of a term.

It is like "splitting" an expression into a multiplication of simpler expressions

6 3*2

10 2*5

20 2*10, 4*5

2555 5*511, 7*365, 35*73

How to find the factorsTo find all the factors

start at 1 and divide your number○ if it can be divided write both 1 and the quotient

move on to the number 2○ again if it can be divided write 2 and the quotient

If not divisible by 2 move on to 3Continue this process until you reach a number you have

already written downYou can skip any numbers you are sure you can not divide

- 76/5 111/2 99/7

Remember we want only whole numbers

What is a factor? Remember that factors are numbers that

you multiply together to reach a product

Factor x Factor = Product

So, factors are numbers that make up a larger number when multiplied together.

What are the common multiples of 3 and 4?

Are there any multiples in common?

Determining common multiples

Multiples of 3 Multiples of 4

1 x 3 = 3 1 x 4 = 4

2 x 3 = 6 2 x 4 = 8

3 x 3 = 9 3 x 4 = 12

4 x 3 = 12 4 x 4 = 16

5 x 3 = 15 5 x 4 = 20

6 x 3 = 18 6 x 4 = 24

7 x 3 = 21 7 x 4 = 28

8 x 3 = 24 8 x 4 = 32

What are the common multiples of 5 and 6? We don’t need to make a chart every time. It is alright to just make a list.

Multiples of 55, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

Multiples of 66, 12, 18, 24, 30, 36, 42, 48, 54, 60

Any multiples in common?

Determining common multiples

Recall: every number has factors (that means two numbers that multiply together to equal that number)

Example: Factors of 121 x 12 = 122 x 6 = 123 x 4 = 12

So, 1, 2, 3, 4, 6, and 12 are all factors of 12

Determining Factors

If two numbers have the same factors, they are said to have common factors.

One way to determine common factors of numbers is to make lists of the factors.

Common Factors – Making Lists

What does this Venn Diagram show us?

What can we learn about common factors from it?

Common Factorsusing Venn Diagrams

With Variables Involved

When you have variables in your terms you will do the number things just like we did. For the variables simply take the least amount of each one.

Factoring out the greatest common monomial factor is the reverse of multiplying a monomial by a polynomial.

Multiply: 3( x + 2 ) = 3x + 6

Factor: 3x + 6 = 3( x + 2 )

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6 3

GCF

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6 3 (

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6 3 (

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6 3 ( x

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6 3 ( x

Factoring Out a Monomial

Examples:

Polynomial Form Factored

3x + 6 3 ( x + 2

Factoring Out a MonomialExamples:

Polynomial Form Factored

3x + 6 3 ( x + 2 )

So…

For each polynomial you will first need to determine the GCF.

Then each terms is divided by the GCF to find the part in the parenthesis.

Factoring Out a Monomial Factor, write prime if prime

1. 6x+3= 3(x+1)

2. 24x -8x= 8x (3x -1)

3. 6x-12= 6(x-2)

4. 2x +8x= 2x(x+4)

5. 4x+10= 2(2x+5)

6. 10x +35x= 5x(2x+7)

7. 10x y-15xy = 5xy(2x-3y)

2

2

2

2 2

2

References Cocarelli, N., 2012. Slideshare. [Online]

Available at: http://www.slideshare.net/naracocarelli/factoring-the-greatest-common-monomial-factor?qid=ccb12499-8de0-4d04-8f4e-61cef2225ef3&v=qf1&b=&from_search=6[Accessed 9 March 2014].

J.Bianco, 2014. Slideshare. [Online] Available at: http://www.slideshare.net/jbianco9910/63-gcf-factoring-day-2[Accessed 9 March 2014].

Noah, A., 2012. Slideshare. [Online] Available at: http://www.slideshare.net/AjarnNoah/factorization-12664260[Accessed 9 March 2014].

T.Bonnar, 2012. Slideshare. [Online] Available at: http://www.slideshare.net/tbonnar/common-multiples-and-common-factors?qid=5cec3e53-792f-4f55-838f-b0f0ec18e59e&v=qf1&b=&from_search=3[Accessed 9 March 2014].

Young, B., 2008. Slideshare. [Online] Available at: http://www.slideshare.net/bayoung/fractions-least-common-multiple-presentation?qid=5cec3e53-792f-4f55-838f-b0f0ec18e59e&v=qf1&b=&from_search=1[Accessed 9 March 2014].