Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Factoring Polynomials: Proficiency Exam

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Elementary Algebra"

    Comments:

    "Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This module is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange GroveAs a part of collection: "Elementary Algebra"

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Elementary Algebra"

    Comments:

    "Elementary Algebra covers traditional topics studied in a modern elementary algebra course. Written by Denny Burzynski and Wade Ellis, it is intended for both first-time students and those […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Factoring Polynomials: Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Factoring is an essential skill for success in algebra and higher level mathematics courses. Therefore, we have taken great care in developing the student's understanding of the factorization process. The technique is consistently illustrated by displaying an empty set of parentheses and describing the thought process used to discover the terms that are to be placed inside the parentheses. The factoring scheme for special products is presented with both verbal and symbolic descriptions, since not all students can interpret symbolic descriptions alone. Two techniques, the standard "trial and error" method, and the "collect and discard" method (a method similar to the "ac" method), are presented for factoring trinomials with leading coefficients different from 1. This module contains a proficiency exam for the chapter "Factoring Polynomials".

Proficiency Exam

Exercise 1

((Reference)) The product is 27 a 3 +9 a 2 +9a 27 a 3 +9 a 2 +9a and a factor is 3a 3a . Find the other factor.

Solution

9 a 2 +3a+3 9 a 2 +3a+3

Exercise 2

((Reference)) The product is 15xn+5y3n2 15 x n 5 y 3 n 2 . Find the other factor.

Solution

5 x n y 2n3 5 x n y 2n3

For the following problems, factor, if possible, the polynomials.

Exercise 3

((Reference)) 14 x 2 y 4 b28 x 2 y 3 b-42 x 2 y 2 14 x 2 y 4 b28 x 2 y 3 b-42 x 2 y 2

Solution

14 x 2 y 2 ( y 2 b+2yb+3 ) 14 x 2 y 2 ( y 2 b+2yb+3 )

Exercise 4

((Reference)) ( y+2 ) a +( y+2 ) c ( y 2 ) a ( y 2 ) c

Solution

( a+c )( y+2 ) ( a+c )( y+2 )

Exercise 5

((Reference)) 6 x 2 y 2 z + 5 x 2 y 3 12 x y z10x y 2 6 x 2 y 2 z 5 x 2 y 3 12 x y z 10x y 2

Solution

xy( xy2 )( 6z+5y ) xy( xy2 )( 6z+5y )

Exercise 6

((Reference)) 4 a 2 16 c 2 4 a 2 16 c 2

Solution

4( a+2c )( a2c ) 4( a+2c )( a2c )

Exercise 7

((Reference)) m 4 n 4 m 4 n 4

Solution

( m 2 + n 2 )( m+n )( mn ) ( m 2 + n 2 )( m+n )( mn )

Exercise 8

((Reference)) b 2 +8b+16 b 2 +8b+16

Solution

( b+4 ) 2 ( b+4 ) 2

Exercise 9

((Reference)) 9 y 2 30 y+25 9 y 2 30 y 25

Solution

( 3y5 ) 2 ( 3y5 ) 2

Exercise 10

((Reference)) x 2 +5x15 x 2 5x 15

Solution

not factorable

Exercise 11

((Reference)) x 2 x30 x 2 x 30

Solution

( x6 )( x+5 ) ( x6 )( x+5 )

Exercise 12

((Reference)) 4 x 6 36 x 4 + 80 x 2 4 x 6 36 x 4 80 x 2

Solution

4 x 2 ( x 2 5 )( x+2 )( x2 ) 4 x 2 ( x 2 5 )( x+2 )( x2 )

Exercise 13

((Reference)) 9 x 2 +25x6 9 x 2 +25x6

Solution

( 9x2 )( x+3 ) ( 9x2 )( x+3 )

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks