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Factoring polynomials is the subject of this algebra lesson




9, 10, 11, 12  

Title – Factoring Polynomials
By – Cristina Bravo
Primary Subject – Math
Secondary Subjects –
Grade Level – 9-12
Time – 2 hours

Overview of Lesson:

    This lesson is intended for algebra students at the middle school or high school level. The lesson will be a direct teaching lesson. With the teacher lecturing and the students taking notes and then having the students break up into groups to solve sample problems.

Content Standard(s):

    4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.


    • Erasers (brought by students)

    • Paper (brought by students)

    • Pencils (brought by students)

    • Worksheets (provided by teacher)

  • Textbook (provided by school)


    For students to learn how to factor successfully difference of two squares, perfect square trinomials, and difference of two cubes.

Lesson Objectives:

    • Students identify and factor binomials that are the differences of squares when given examples.

    • Students identify and factor perfect square trinomials when given examples.

  • Students identify and factor difference of two cubes when given examples.

Skills Provided:

    • Students have a strong background in prime factorizations of integers.

    • Students have a strong background in finding greatest common factors (GCF) for sets of monomials.

  • Students have a strong background in finding GCF and the distributive property to factor polynomials.
  • Students have a strong background in grouping to factor polynomials with 4+ terms.

Suggested Procedures:

    • Students come in and take mini quiz on finding GCF and prime factorization. (10 minutes)
    • Go over material from previous day and go over key vocabulary for the pertaining to the new lesson. (20 minutes)
    • Students begin to take notes on new material (35 minutes).

    • Clarify any questions (10 minutes).

  • Students have 30 minutes to work in groups and finish worksheets.

Opening of the Lesson:

    After students have taken mini quiz. Teacher will go over previous material learned and new vocabulary with the students.

Specific Activities:

    Worksheet that is attached.


    Last 15 minutes students write in their math journal about how the old concepts learned in the class has helped them with the new material.


    • Collect their assignments and review their work to check for assessment.

    • Collect student’s journals to see what they have written about the connection between old material and new material.

  • Give students a mini quiz on the material the next day.

Extension of the Lesson:

    Assigning homework to the students covering the new material.

Resources Necessary:

  • Math textbook for completing homework assignment.

Factoring Worksheet

1. Factor: x 2 -9

2. Factor: a 2 -36

3. Factor: 9y 2 -81

4. Factor: 16y 6 -25x 2

5. Factor: a 2 – (1/9)

6. Factor: 5-5x 2 y 6

7. Factor: 16yx 4 -81y

8. Factor: x 2 -10x+25.

9. Factor: 16y 2 +56y+49

10. Factor: 2x 2 -12xy+18y 2

11. Factor: -4y 2 -144y 8 +48y 5

12. Factor: x 3 -27

13. Factor: 125x 3 +y 3

14. Factor: 128y 7 -250yx 6

15. Factor: z 3 +27

16. Factor: 64y 3 +1

17. Factor: 5x 3 -40z 3

18. Factor: 2y 4 -128y

E-Mail Cristina Bravo !

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