xyAlgebra Topic Examples

A. Signed Number Operations
B. Expression Evaluation
C. Simplifying Polynomials
D. Factoring
E. Algebraic Fractions
F. Polynomial Long Division
G. Solving Linear Equations
H. Plotting and Graphing


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D. Factoring

   a. Common Factors (Note: Only 2 problems each if student solves them correctly)
      1. Review: Multiplication
      2. Removing Common Factors
      3. Removing Common Factors (2)
      4. Removing Common Factors (3)
      5. Removing Common Factors (4)
      6. Removing Common Factors (5)
      7. Removing Common Factors (6)
      8. Removing an Entire Term
      9. Removing Common Factors (7)
      10. Removing Common Factors (8)

   b. Difference of Squares (Note: 2-3 problems each if student solves them correctly)
      11. Review: (a+b)(a-b) Again
      12. Factoring Differences of Squares
      13. Factoring Differences of Squares (2)
      14. Factoring Differences of Squares (3)
      15. Removing Common Factors First
      16. Factoring Differences of Squares (4) (Note: Answers are 3 parentheses long)
      17. Factoring Review

   c. Monic Trinomials (Note: 2-3 problems each if students solves them correctly)
      18. Review: Multiplication (2)
      19. Factoring Three Terms
      20. Factoring Three Terms (2)
      21. Factoring Three Terms (3)
      22. Factoring Three Terms (4)
      23. Factoring Three Terms (5)
      24. Factoring Three Terms (6)
      25. Factoring Three Terms (7)
      26. Factoring Three Terms (8)
      27. Factoring Three Terms (9)
      28. Factoring Three Terms (10)
      29. Removing Common Factors First (2)
      30. Rearranging Terms for Factoring
      31. Rearranging Terms for Factoring (2)

   d. Parenthesized Common Factors (Note: 2 problems each if student solves them correctly)
      32. Parenthesized Common Factors
      33. Parenthesized Common Factors (2)
      34. Parenthesized Common Factors (3)
      35. Removing an Entire Term (2)
      36. Removing All But a Minus Sign

   e. Four Terms (1-5 problems each if correct)
      37. Review: Multiplication (3)
      38. Factoring Four Terms
      39. Factoring Four Terms (2) (Note: 1 problem)
      40. Factoring Four Terms (3)
      41. Factoring Four Terms (4)
      42. Factoring Four Terms (5)
      43. Factoring Four Terms (6) (Note: 3-factor answers)
      44. When Can Four Terms Be Factored?
      45. Unfactorable Expressions
      46. Rearranging Four Terms
      47. Factoring Four Terms (7)
      48. Removing Common Factors First (3)

   f. Non-monic Trinomials
      49. Factoring Three Terms (11)
      50. Factoring Three Terms (12)
      51. Factoring Three Terms (13)
      52. Factoring Three Terms (14)
      53. Factoring Three Terms (15)
      54. Factoring Three Terms (16)
      55. Factoring Three Terms (17)
      56. Factoring Three Terms (18)

   g. Sum of Cubes
      57. Factoring A Sum of Cubes
      58. Factoring A Sum of Cubes (2)

   h. Difference of Cubes
      59. Factoring A Difference of Cubes
      60. Factoring A Difference of Cubes (2)



Examples

D. Factoring

   a. Common Factors (Note: Only 2 problems each if student solves them correctly)
      1. Review: Multiplication

2. Removing Common Factors

3. Removing Common Factors (2)

4. Removing Common Factors (3)

5. Removing Common Factors (4)

6. Removing Common Factors (5)

7. Removing Common Factors (6)

8. Removing an Entire Term

9. Removing Common Factors (7)

10. Removing Common Factors (8)

b. Difference of Squares (Note: 2-3 problems each if student solves them correctly) 11. Review: (a+b)(a-b) Again

12. Factoring Differences of Squares

13. Factoring Differences of Squares (2)

14. Factoring Differences of Squares (3)

15. Removing Common Factors First

16. Factoring Differences of Squares (4) (Note: Answers are 3 parentheses long)

17. Factoring Review

c. Monic Trinomials 18. Review: Multiplication (2)

19. Factoring Three Terms

20. Factoring Three Terms (2)

21. Factoring Three Terms (3)

22. Factoring Three Terms (4)

23. Factoring Three Terms (5)

24. Factoring Three Terms (6)

25. Factoring Three Terms (7)

26. Factoring Three Terms (8)

27. Factoring Three Terms (9)

28. Factoring Three Terms (10)

29. Removing Common Factors First (2)

30. Rearranging Terms for Factoring

31. Rearranging Terms for Factoring (2)

d. Parenthesized Common Factors (Note: 2 problems each if student solves them correctly) 32. Parenthesized Common Factors

33. Parenthesized Common Factors (2)

34. Parenthesized Common Factors (3)

35. Removing an Entire Term (2)

36. Removing All But a Minus Sign

e. Four Terms (1-5 problems each if correct) 37. Review: Multiplication (3)

38. Factoring Four Terms

39. Factoring Four Terms (2) (1 problem)

40. Factoring Four Terms (3)

41. Factoring Four Terms (4)

42. Factoring Four Terms (5)

43. Factoring Four Terms (6) (3-factor answers)

44. When Can Four Terms Be Factored?

45. Unfactorable Expressions

46. Rearranging Four Terms

47. Factoring Four Terms (7)

48. Removing Common Factors First (3)

f. Non-monic Trinomials 49. Factoring Three Terms (11)

50. Factoring Three Terms (12)

51. Factoring Three Terms (13)

52. Factoring Three Terms (14)

53. Factoring Three Terms (15)

54. Factoring Three Terms (16)

55. Factoring Three Terms (17)

56. Factoring Three Terms (18)

g. Sum of Cubes 57. Factoring A Sum of Cubes

58. Factoring A Sum of Cubes (2)

h. Difference of Cubes 59. Factoring A Difference of Cubes

60. Factoring A Difference of Cubes (2)

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Compiled by Eric Ferrante. Send comments or suggestions to ferrante@MrFerrante.com

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