Throughout this unit we will study Polynomials and Factoring.   Polynomials are among the first mathematical models to be used, and this unit will explore these models in order to demonstrate how they relate to each other by addition, subtraction, or multiplication.  The students will be able to classify a polynomial by degree and by numbers of terms and use this knowledge to add, subtract, and multiply polynomials.   By spending a greater quantity of time on multiplying polynomials using the distributive property, the FOIL pattern, the sum and difference pattern, and the square of a binomial pattern the students will be able to use this knowledge and apply it to factoring.   Factoring a polynomial, or the process of "undoing" multiplication, will be shown in three stages: using the difference of two squares pattern, using the perfect square pattern, and using the guess-and-check strategy.  At the conclusion of this unit the students will be able to make connections and begin to build mathematical relationships.  Furthermore, the students will be able to apply this newly acquired knowledge to real world problems and practice their problem solving skills.
 

Objectives

• The students will add, subtract, and multiply polynomials using concrete objects, pictorial representations, and algebraic manipulations. (A.11)
• The students will factor completely first- and second- degree binomials and trinomials in one or two variables.  The graphing calculator will be used as a tool for factoring and for confirming an algebraic factorization. (A.12)

• Visual for adding and subtracting like terms
• Puzzles for adding and subtracting polynomials
• Handouts of the steps and rules used in multiplying polynomials and factoring polynomials
• Worksheets for guided and individual assignments

Click here to view detailed lesson plans:

 Adding and Subtracting Polynomials

 Multiplying Polynomials: Two Special Cases

 Factoring Quadratic Trinomials