Zach

Paul

Start

Step 1

Is there a Greatest Common Factor?

Yes No

Example

Step 1 Continued

Factor out the Greatest Common Factor.

Next Step

Last StepExample

Step 2

How many terms are in the polynomial?

2 3 4 or more

Last StepExample

Step 3

Is the leading coefficient one?

Yes No

Last StepExample

Step 3 continued

Find factors of third term that add up to the middle term.

Next

Last StepExample

Step 3 continuedFollow these steps:

Multiply the leading coefficient and the constantFind factors of that number that add up to the middle coefficientRewrite the middle term using these factorsFactor by using Grouping Method

Next

Last StepExample

Step 3

Is there a difference of two squares?

Yes No

Last StepExample

Step 3 continued

Use the Sum and Difference pattern to finish factoring.

Next

Last StepExample

Step 3

Use the Grouping Method to finish factoring the polynomial.

Next

Last StepExample

Congratulations

You have factored the polynomial as much as possible.

Restart

Greatest Common Factor Examples

With a GCF: Without a GCF.

5 4 32 2 4x x x

Has a GCF of32x

212 7 1x x

Has no common factors other than 1

Back to Problem

How to Factor Out a Greatest Common Factor

Back to Problem

5 4 32 2 4x x x

Take the GCF and factor (divide each term by that number).

3 22 ( 2)x x x

Examples with Different Numbers of Terms

Back to Problem

2 Terms 3 Terms 4 Terms

225 4x 2 2x x 3 23 4 12x x x

Leading Coefficient Examples

Back to Problem

Leading Coefficient of 1 Other than 1

2 4x 24 4x

Factoring Example

Back to Problem

2 8 15

( 5)( 3)

x x

x x

2 8 15

( 5)( 3)

x x

x x

Find factors of last term (15) that add up to middle term (8). (these would be 5 and 3)

Factoring Example

Back to Problem

Multiply the leading coefficient and the constant (12 X 1)Find factors of that number that add up to the middle coefficient (4 and 3)Rewrite the middle term using these factors

Factor by using Grouping Method

212 7 1x x

212 4 3 1x x x

Squares Example

Back to Problem

225 4x

difference Perfect squarePerfect Square

Sum and Difference

Back to Problem

225 4x

(5 2)(5 2)x x

Use the SUM and DIFFERENCE of the two squares.

Grouping Method

Back to Problem

3 2

3 2

2

2

2 16 32

( 2 ) ( 16 32)

( 2) ( 16)( 2)

( 2)( 16)

x x x

x x x

x x x

x x

Group Terms

Factor Each Group

Use Distributive Property

Grouping Method

Back to Example

3 2

3 2

2

2

2 16 32

( 2 ) ( 16 32)

( 2) ( 16)( 2)

( 2)( 16)

x x x

x x x

x x x

x x

Group Terms

Factor Each Group

Use Distributive Property