Flip Book

Factoring Polynomials

This  flipbook  is  great  for  an  interac3ve  notebook,  as  a  study  guide,  or  as  class  notes  through  a  factoring  unit.        This  flipbook  is  given  in  two  different  ways:    filled  in  and  fill-­‐in-­‐the-­‐blank.    There  is  plenty  of  room  for  students  to  work  the  problems  in  whichever  way  is  preferred.      

   

Copying  Direc-ons    To  copy  the  flipbook,  turn  every  other  page  upside  down,  like  the  photos.  

©  2014    Mrs.  E  Teaches  Math  

©  2014    Mrs.  E  Teaches  Math  

Assembly  Direc-ons    First,  fold  the  cover  sheet  along  the  doBed  line.    It  should  look  like  the  photo  below.                      Then,  find  the  sheet  that  says  “Greatest  Common  Factor”  at  the  boBom.    Fold  this  sheet  along  the  doBed  line.  

©  2014    Mrs.  E  Teaches  Math  

Put  the  second  folded  sheet  inside  the  cover  sheet.    It  should  look  like  the  photo  below.                              Fold  the  last  sheet  along  the  doBed  line.  

©  2014    Mrs.  E  Teaches  Math  

Put  the  third  folded  sheet  inside  the  other  two  sheets  to  complete  the  flip  book.    It  should  look  like  the  photo  below.                          

©  2014    Mrs.  E  Teaches  Math  

Answer  Key    

The  answer  key  is  displayed  in  the  order  of  the  flaps.  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Answer  Key  

©  2014    Mrs.  E  Teaches  Math  

Factoring Polynomials

Name __________________

©  2014      Mrs.  E  Teaches  Math  

Factored Completely – factor until all factors other than monomials factors are prime factors Prime – factors that cannot be factored completely The greatest common factor (GCF) is the largest factor that two terms have in common.

Factoring by Grouping

Example - Factor out the GCF: 2x − 2 Example - Factor out the GCF: 7x2 +14

Practice – Factor each polynomial. a) b) c) d) e) f) g) h)

12x3 − 21x2 + 28x − 49

49x3 − 35x2 + 56x − 40

4x3 +15− 5x −12x2 x

3 + 4x2 + 3x +12

4xy + 6− x − 24y

3x3 + 3x2 − 8x − 8

xy − 5y − 2x +10 −24 − 4x + x2 + 6x

Greatest Common Factor

Practice – Factor out the GCF. a) b) c) d) e) f)

3x − 3

18x3 + 27x2

x4 + x2

3x2 +12x + 9

x2 x + 3( ) + 5 x + 3( )

x2 x − 2( )− x − 2( )

Some polynomials only have a GCF of 1. However, by grouping the terms, it still may be possible to factor. Examples – Factor by grouping. a) b) c) d) e) f)

x3 − x2 − 5x + 5

12x2y − 27y − 4x2 + 9

x3 − 2x + 5x2 −10

3x + 7y − 21− xy

8x3 − 64x2 + x − 8

42xy + 36xz − 7w 2y − 6w 2z

Special Factoring Patterns

Examples – Factor each trinomial. a) b) c) d) x

2 + 2x +1

x2 + 6x + 8 x

2 + 3x − 28

x2 − 2x −15

Practice – Factor each polynomial. a) b) c) d) e) f)

x4 − 81

216+ x3

81x2 −16

16x2 − 56x + 49

x3 + 8

16x2 − 48x + 36

Factoring Trinomials x2 + bx + c

Practice – Factor each trinomial. a) b) c) d) e) f)

x2 +13x + 40 x

2 + 3x −18

x2 − 5x −14 x

2 − 4x − 5

x2 − x −12 x

2 + 3x − 88

Difference of Two Squares Perfect Square Trinomials Sum or Difference of Two Cubes Examples – Factor each polynomial. a) b) c) d)

a2 + 2ab +b2 = a +b( )2a2 − 2ab +b2 = a −b( )2

a2 −b2 = a +b( ) a −b( )

x2 − 4

81x2 − 49

27x3 +1

25x2 − 60x + 36

a3 +b3 = a +b( ) a2 − ab +b2( )a3 −b3 = a −b( ) a2 + ab +b2( )

Factoring Trinomials ax2 + bx + c

Examples – Factor each trinomial. a) b) c) d)

3x2 − x − 2 6x2 − 7x − 5

8x2 −10x − 3 15x2 −19x + 6

Practice – Factor each trinomial. a) b) c) d) e) f)

6x2 +19x − 7 2x2 − 7x + 3

3x2 −13x + 4 2x2 + x − 3

6x2 + 7x −10 2x2 − 9x − 5

This  page  is  inten3onally  leI  blank.    The  flipbook  aIer  this  page  is  the  fill-­‐in-­‐the-­‐blank  version.  

©  2014    Mrs.  E  Teaches  Math  

Factoring Polynomials

Name __________________

©  2014      Mrs.  E  Teaches  Math  

Factored Completely – factor until all factors other than _____________ factors are ____________ factors Prime – The greatest common factor (GCF) is the ______________ factor that two ___________ have in common.

Factoring by Grouping

Example - Factor out the GCF: 2x − 2 Example - Factor out the GCF: 7x2 +14

Practice – Factor each polynomial. a) b) c) d) e) f) g) h)

12x3 − 21x2 + 28x − 49

49x3 − 35x2 + 56x − 40

4x3 +15− 5x −12x2 x

3 + 4x2 + 3x +12

4xy + 6− x − 24y

3x3 + 3x2 − 8x − 8

xy − 5y − 2x +10 −24 − 4x + x2 + 6x

Greatest Common Factor

Practice – Factor out the GCF. a) b) c) d) e) f)

3x − 3

18x3 + 27x2

x4 + x2

3x2 +12x + 9

x2 x + 3( ) + 5 x + 3( )

x2 x − 2( )− x − 2( )

Some polynomials only have a GCF of __________. However, by _______________ the terms, it still may be possible to factor. Examples – Factor by grouping. a) b) c) d) e) f)

x3 − x2 − 5x + 5

12x2y − 27y − 4x2 + 9

x3 − 2x + 5x2 −10

3x + 7y − 21− xy

8x3 − 64x2 + x − 8

42xy + 36xz − 7w 2y − 6w 2z

Special Factoring Patterns

Examples – Factor each trinomial. a) b) c) d) x

2 + 2x +1

x2 + 6x + 8 x

2 + 3x − 28

x2 − 2x −15

Practice – Factor each polynomial. a) b) c) d) e) f)

x4 − 81

216+ x3

81x2 −16

16x2 − 56x + 49

x3 + 8

16x2 − 48x + 36

Factoring Trinomials x2 + bx + c

Practice – Factor each trinomial. a) b) c) d) e) f)

x2 +13x + 40 x

2 + 3x −18

x2 − 5x −14 x

2 − 4x − 5

x2 − x −12 x

2 + 3x − 88

Difference of Two Squares Perfect Square Trinomials Sum or Difference of Two Cubes Examples – Factor each polynomial. a) b) c) d)

a2 + 2ab +b2 =a2 − 2ab +b2 =

a2 −b2 =

x2 − 4

81x2 − 49

27x3 +1

25x2 − 60x + 36

a3 +b3 =a3 −b3 =

Factoring Trinomials ax2 + bx + c

Examples – Factor each trinomial. a) b) c) d)

3x2 − x − 2 6x2 − 7x − 5

8x2 −10x − 3 15x2 −19x + 6

Practice – Factor each trinomial. a) b) c) d) e) f)

6x2 +19x − 7 2x2 − 7x + 3

3x2 −13x + 4 2x2 + x − 3

6x2 + 7x −10 2x2 − 9x − 5

Need  more  ideas  for  your  factoring  unit?  

   Mrs.  E  Teaches  Math  Blog  Posts  Factoring  with  Symbols  Factoring  Prac3ce!  Incorpora3ng  Wri3ng  in  Math      Mrs.  E  Teaches  Math  Products  •FREE•  Mul3plying  and  Factoring  Polynomials  Matching  Cards  Solving  Quadra3c  Equa3ons  by  Factoring  Task  Cards  

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