Intro W9

• 1. Current Page: Intro W9 (1 of 14)
  2. Resources W9 (2 of 14)
  3. TN W9, Assignment (3 of 14)
  4. 7.1 Video Lesson, Assignment (4 of 14)
  5. 7.1 Practice, Assignment (5 of 14)
  6. 7.1 Video Lesson, Assignment (6 of 14)
  7. 7.1 Practice, Assignment (7 of 14)
  8. 7.2 Video Lesson, Assignment (8 of 14)
  9. 7.3 Video Lesson, Assignment (9 of 14)
  10. 7.2, 7.3 Practice, Assignment (10 of 14)
  11. 7.4 Video Lesson, Assignment (11 of 14)
  12. 7.4 Practice, Assignment (12 of 14)
  13. Outro W9 (13 of 14)
  14. Collaboration 2, Assignment (14 of 14)

        Intro W9

  •  Objectives

    1. Quadratic expressions may be used to model physical properties of a large bridge, the trajectory of a baseball or rocket, and revenue and profit of a business. By factoring these expressions, specific characteristics of the model can be identified. In this chapter, you will explore the process of factoring expressions and see how factoring is used to solve certain types of equations.

       In this chapter, we will look at methods to solve situations like these using equations with two variables.

    3. The sections for this week are:
       • 7.1 Greatest Common Factor and Factor by Grouping
       • 7.2 Factor Trinomials of the Form x2+bx+c
       • 7.3 Factor Trinomials of the Form ax2+bx+c
       • 7.4 Factor Special Products
       • 7.5 General Strategy for Factoring Polynomials

   

   Intro and Learning Objectives (click on all tabs to see all sections)

  • • 7.1
    • 7.2
    • 7.3
    • 7.4
    • 7.5

     Learning Outcomes

    In this section, you will:

    • Find the greatest common factor of two or more expressions
    • Factor the greatest common factor from a polynomial
    • Factor by grouping

     Intro

    Earlier we multiplied factors together to get a product. Now, we will be reversing this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called factoring. We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the greatest common factor of two or more expressions. The method we use is similar to what we used to find the LCM.

     Learning Outcomes

    In this section, you will:

    • Factor trinomials of the form x2+bx+c
    • Factor trinomials of the form x2+bxy+cy2

     Intro

    1. Step 1. Write the factors as two binomials with first terms x: (x     )(x     ).
    2. Step 2. Find two numbers m and n that
        Multiply to c, m⋅n=c
        Add to b, m+n=b
    3. Step 3. Use m and n as the last terms of the factors: (x+m)(x+n).
    4. Step 4. Check by multiplying the factors.

     Learning Outcomes

    In this section, you will:

    • Recognize a preliminary strategy to factor polynomials completely
    • Factor trinomials of the form ax2+bx+c with a GCF
    • Factor trinomials using trial and error
    • Factor trinomials using the ‘ac’ method

     Intro

    Now we are ready to factor trinomials whose leading coefficient is not 1, trinomials of the form ax2+bx+c.

    Remember to always check for a GCF first! Sometimes, after you factor the GCF, the leading coefficient of the trinomial becomes 1 and you can factor it by the methods in the last section. What happens when the leading coefficient is not 1 and there is no GCF? There are several methods that can be used to factor these trinomials. First we will use the Trial and Error method and then the "ac" method.

     Learning Outcomes

    In this section, you will:

    • Factor perfect square trinomials
    • Factor differences of squares
    • Factor sums and differences of cubes
    • Choose method to factor a polynomial completely

     Intro

    The strategy for factoring we developed in the last section will guide you as you factor most binomials, trinomials, and polynomials with more than three terms. We have seen that some binomials and trinomials result from special products—squaring binomials and multiplying conjugates. If you learn to recognize these kinds of polynomials, you can use the special products patterns to factor them much more quickly.

     Learning Outcomes

    In this section, you will:

    • Recognize and use the appropriate method to factor a polynomial completely

     Intro

    You have now become acquainted with all the methods of factoring that you will need in this course. Here is a strategy you should use when factoring polynomials.

    1. Step 1. Is there a greatest common factor?
       • Factor it out.
    2. Step 2. Is the polynomial a binomial, trinomial, or are there more than three terms?
       • If it is a binomial:
         Is it a sum?
         • Of squares? Sums of squares do not factor.
         • Of cubes? Use the sum of cubes pattern.
         Is it a difference?
         
         • Of squares? Factor as the product of conjugates.
         • Of cubes? Use the difference of cubes pattern.
       • If it is a trinomial:
         Is it of the form x2+bx+c? Undo FOIL.
         Is it of the form ax2+bx+c?
         
         • If a$a$ and c$c$ are squares, check if it fits the trinomial square pattern.
         • Use the trial and error or “ac” method.
       • If it has more than three terms:
         Use the grouping method.
    3. Step 3. Check.
       • Is it factored completely?
       • Do the factors multiply back to the original polynomial?

     Readings

    1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
    2. Videos: Watch all the videos from "Resources W9"

     Assignments

    • Take Notes Week 9         Due Friday night.
      

    Directions

    •  Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:

    • • Your name
      • The name of the section
      • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
      • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
      • You have to solve ALL "Try It" exercises.

    After you complete your notes you have to submit them. See Take Notes Methods. 

     

    • Video quizzes Week 9          Due Saturday night 11:59pm.

    Directions

    • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

     

    • Homework Week  9              Due Sunday night 11:59pm.
    •  

    Directions

    • There are 4 Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

    • Collaborations 2

  The due dates for assignments are Friday, Saturday, and Sunday.

  However, you can submit them until Tuesday night next week.

  A 5% per day penalty applies for late work if you'll do it until Tuesday night.