2.08   Review of Factoring

from Basic Algebra: One Step at a Time © 2002

P. 181-184

Dr. Robert J. Rapalje

Seminole Community College

 

ANSWERS TO ALL EXERCISES ARE INCLUDED AT THE END OF THIS PAGE

 

To see selected solutions in Living C O L O R  click here!

 

Having just completed several sections of factoring exercises, it is a good idea to put it all together in a summary review.  This is essential, especially considering the importance of factoring to concepts yet to come.

EXERCISES.       In each of the following, factor completely.  Show all necessary steps.

 1.        x2  −  16                                    2.        x2  −  49                                    3.        x2  −   9x

    = (          )(          )                                 =  (            )(            )                              = ____(              ) 

 

 4.        x2  −  81                                    5.        x2  −  100                                  6.        x2  −   64

 

 

 7.        x2 −  36y2                                  8.        x2 + 7x + 10                             9.        x2 − 7x − 8

 

 

10.       4x2 − 9 y2                                 11.       16x2 − 1                                   12.       x2 + 2xy + y2

 

     

13.       x2 − 36                                     14.   a(a−b) + b(a−b) + c(a−b)             15.       x3 − 36x2 

             

 

16.       x2 − 12x + 36                          17.       x2 − 3x − 10                            18.       x2 + 10x +25

 

 

19.       x2 − 5x + 6                              20.       x2 − x − 90                              21.       x2 + 19x + 34

 

 

22.       −12x2 − 6x                              23.       x2 − 18x + 45                          24.       x2 + 4x − 45

 

 

25.      n(n−1) + 2(n−1)                        26.       25x2 − 40x                               27.       9x2 − 25y2

 

 

28.       3x2 + 12xy                               29.       9 − 4x2                                     30.       x3 + 7x2       

    

 

31.       x2 + 23x + 120                        32.       3x2 + 29x + 40                        33.       x2 + 4xy + 3y2

 

        

34.       n2 + 9n − 10                             35.       27n2 − 90mn                            36.       x2 + 21x + 54             

 

 

 

Exercises 37 − 66, require two or more steps!  Remember to factor the common factor first!

37.       3x2 + 12x + 12                        38.       x2y − 25y                                 39.       x4 − 1 

    = ____(                       )                     = ____(                    )                       =  (              )(               )

    = ____(            )(            )                  = ____(             )(             )              = (          )(          )(              )

    = ____(             )2

 

40.       x3 − 2x2 + 4x − 8                     41.       x3 − 2x2 − 4x + 8                     42.       5x3 − 20x

     = x2(            ) + 4 (           )

   =  (               )(               )

 

43.       x3  −   x                              44.    3x2 + 39x + 120                            45.   10x2 + 30x − 540

 

 

 

 

46.       x3 + 6x2 − 7x                      47.    4x2 − 8x − 60                               48.   x2(x−2) − 16(x−2)   

 

 

 

 

49.       100x2 − 25y2                        50.    3x2 − 75                                        51.    2x2 − 32x + 30

 

 

 

 

52.       2x2 − 32                                53.     x3 + 8x2 − 9x − 72                      54.     15x4 − 60x2

 

 

 

 

55.       15x2 − 60y2                           56.    x2 + 24x + 144                           57.    9x2  − 9

 

 

 

 

58.       x3 + 3x2 − 25x − 75              59.     x3 + 7x2 + 10x                          60.    x3 + 8x2 + 16x

 

 

 

 

61.       x3 − 4x2 − 16x + 64             62.     x3 + 2x2 − 4x − 8                      63.     x4 − 16                                          

                          

 

 

64.       x2y2 − xy2 − 2y2                   65.     3x3y + 21x2y + 30xy                 66.    x4 − 13x2 + 36

 

 

 

ANSWERS 2.08

p. 181-184:      (NOTE:  Factors may be given in any order!)

              1. (x-4)(x+4);  2. (x-7)(x+7);  3.  x(x-9);  4. (x-9)(x+9);  5. (x-10)(x+10); 

              6. (x-8)(x+8);  7. (x-6y)(x+6y);  8. (x+2)(x+5);  9. (x-8)(x+1);   10. (2x-3y)(2x+3y);

            11.  (4x-1)(4x+1);   12. (x+y)2;   13. (x-6)(x+6);   14. (a-b)(a+b+c);    15. x2(x-36);

            16.  (x-6)2; 7. (x-5)(x+2); 18. (x+5)2; 19. (x-2)(x-3); 20. (x-10)(x+9);   21. (x+17)(x+2);

            22. -6x(2x+1);  23. (x-15)(x-3);  24. (x+9)(x-5);  25. (n-1)(n+2);   26. 5x(5x-8);  

            27. (3x-5y)(3x+5y);  28. 3x(x+4y);  29. (3-2x)(3+2x); 30. x2(x+7);   31. (x+8)(x+15);

            32. (3x+5)(x+8); 33. (x+3y)(x+y); 34. (n+10)(n-1); 35. 9n(3n-10m);  36. (x+18)(x+3);         

            37.  3(x+2)2;  38. y(x-5)(x+5);  39.  (x-1)(x+1)(x2+1);  40.  (x-2)(x2+4);

            41.  (x-2)2(x+2);  42. 5x(x-2)(x+2); 43. x(x-1)(x+1); 44. 3(x+8)(x+5); 45. 10(x+9)(x-6);     

            46.  x(x+7)(x-1);  47. 4(x-5)(x+3);   48. (x-2)(x-4)(x+4); 49. 25(2x-y)(2x+y);

            50.  3(x-5)(x+5); 51. 2(x-15)(x-1);  52. 2(x-4)(x+4);  53. (x+8)(x-3)(x+3);  

            54.  15x2(x-2)(x+2);   55. 15(x-2y)(x+2y); 56. (x+12)2;   57. 9(x-1)(x+1);

            58.  (x+3)(x-5)(x+5);  59. x(x+5)(x+2);  60. x(x+4)2;  61. (x-4)2(x+4);  62. (x+2)2(x-2);       

            63.  (x-2)(x+2)(x2+4); 64. y2(x-2)(x+1); 65. 3xy(x+5)(x+2);   66. (x-3)(x+3)(x-2)(x+2).

 

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Dr. Robert J. Rapalje Altamonte Springs Campus
Contact me at:   rapaljer@scc-fl.edu
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