# Ch 6: Common Core HS Algebra: Polynomials

Watch our lessons on high school algebra. These lessons meet the Common Core Mathematics standards for polynomials (CCSS.Math.Content.HSA-APR.A.1; CCSS.Math.Content.HSA-APR.B.2; CCSS.Math.Content.HSA-APR.B.3; CCSS.Math.Content.HSA-APR.C.4; CCSS.Math.Content.HSA-APR.C.5; CCSS.Math.Content.HSA-APR.D.6).

Standards Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (CCSS.Math.Content.HSA-APR.A.1)

Standards Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). (CCSS.Math.Content.HSA-APR.B.2)

Standards Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (CCSS.Math.Content.HSA-APR.B.3)

Standards Prove polynomial identities and use them to describe numerical relationships. (CCSS.Math.Content.HSA-APR.C.4)

Standards Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. (CCSS.Math.Content.HSA-APR.C.5)

Standards Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. (CCSS.Math.Content.HSA-APR.D.6)

Students who have mastered this standard will be able to add, subtract and multiply polynomials with ease. They will also be able to divide polynomials using long or synthetic division. Those who complete this chapter will develop enough skills to comfortably rewrite some rational expressions.

Lessons in this standard cover concepts such as:

• Defining what a polynomial is
• Understanding concepts related to polynomial identities and combinatorics
• Using the binomial theorem and remainder theorem
• Multiplying binomials
• Constructing graphs using the zeros of polynomials

Students demonstrate mastery of these standards when they can explain the relationship between the factors and zeros of polynomials, perform arithmetic operations on polynomials and solve problems with polynomial identities. Mastering these standards can help support preparedness for any future course or career that deals with solving problems that feature unknown variables.

### How to Use These Lessons in Your Classroom

Here are some tips for how to use the lessons to support instruction in these standards:

#### Adding, Subtracting, Multiplying and Dividing Polynomials Lessons

Develop a worksheet that covers adding, subtracting, multiplying and dividing polynomials. Display the video lessons covering the concepts from the worksheet. Assign the worksheet for the students to complete for homework. Before your students turn in the assignment, go over each problem to make sure they understand each type of operation.

#### Pre-Quiz and Post-Quiz Lessons

In order to highlight the important concepts found in this chapter, have your students take the lesson quizzes before diving into the chapter content. Spend the next few classes investigating the concepts found in the chapter lessons. After the students finish the lessons, require them to complete the quizzes to assess their information retention.

#### Constructing a Graph by Using Zeros Lessons

Create a worksheet requiring students to find the zeros of polynomials and show the video lessons 'Finding Zeros of Polynomials by Factoring' and 'Using Zeros to Construct a Graph.' Have the students complete the worksheet for homework. During the next class, pass out graph paper and require the students to graph the zeroes that they found on the worksheet.

7 Lessons in Chapter 6: Common Core HS Algebra: Polynomials
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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