In this chapter, students add, subtract, multiply, and simplify polynomials. Students learn to recognize special products of binomials and then move on to factoring trinomials.
Addition and Subtraction of Polynomials -
Multiplication of Polynomials -
Special Products of Polynomials -
Polynomial Equations in Factored Form -
Factoring Quadratic Expressions -
Factoring Special Products -
Factoring Polynomials Completely -
Problem-Solving Strand for Mathematics
In this chapter, Factoring Polynomials, our exploration is focused on the problem-solving techniques Make a Systematic List and Draw a Picture/Use a Model (Visualizing).
The FlexBook® textbook repeatedly illustrates systematic lists of possible factors, particularly in lessons Factoring Quadratic Expressions, Factoring Special Products, and Factoring Polynomials Completely. When working with these lessons, point out the organizational scheme the authors have used to list all possible factors; this can be enlightening and give students a model from which to work. By making a systematic list, students begin to see patterns that can help them make better “educated guesses.” An organized list will also help them find all possibilities.
The use of a systematic list applies in this unit not only to the sets of possible factors and the signs of these factors, but also to the techniques that should be applied before deciding whether or not a polynomial is prime.
Alignment with the NCTM Process Standards
Among the NCTM Process Standards, Communication, Connections, and Representation are most directly represented in this unit. By making a systematic, orderly list, students organize and consolidate their mathematical thinking (COM.1) and communicate their thinking coherently and clearly to peers and teachers (COM.2). Through classroom discussions and sharing approaches and projects, they will analyze and evaluate the mathematical thinking and strategies of others (COM.3) and will recognize and use connections between algebraic and geometric representations (CON.1). The tree diagrams, tables, charts, and matrices that students create to organize, record, and communicate mathematical ideas (R.1) are excellent tools for displaying data systematically. In studying the illustrations provided in the FlexBook® textbook and developing their own visualizations and models, students will have the opportunity to select, apply, and translate among mathematical representations (R.2) and to use representations to model and interpret physical, social, and mathematical phenomena (R.3).
- COM.1 - Organize and consolidate their mathematical thinking through communication.
- COM.2 - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
- COM.3 - Analyze and evaluate the mathematical thinking and strategies of others.
- CON.1 - Recognize and use connections among mathematical ideas.
- R.1 - Create and use representations to organize, record, and communicate mathematical ideas.
- R.2 - Select, apply, and translate among mathematical representations to solve problems.
- R.3 - Use representations to model and interpret physical, social, and mathematical phenomena.