The purpose of this task is to emphasize the use of the …

The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.

In the world of mathematics you can always count on encountering problems …

In the world of mathematics you can always count on encountering problems involving multiplication. With polynomials, things are no different. It is imperative to look at various types of multiplication problems since there are many different polynomials such as: monomials, binomials, trinomials, and more. This seminar covers the various forms of multiplication with these different types of polynomials.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.

Overview: This is a PBL project as part of an Integrated Math course with …

Overview: This is a PBL project as part of an Integrated Math course with a focus on Functions and Functional Relationships related to Polynomials. The overarching objective of the project is for the student to recognize, describe, model, manipulate, use, and solve non-linear functional relationships to compare the characteristics of different function types. Through the application of these concepts, students will better understand the nature and structure of functions, especially as they pertain to polynomials, exponential functions, variation, and transformations. Note that the project was designed and delivered per the North Carolina Math 2 curriculum, but can be customized to meet your own specific curriculum needs.

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook …

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

In this project, you will explore a real-world problem, and then work …

In this project, you will explore a real-world problem, and then work through a series of steps to analyze that problem, research ways the problem could be solved, then propose a possible solution to that problem. Often, there are no specific right or wrong solutions, but sometimes one particular solution may be better than others. The key is making sure you fully understand the problem, have researched some possible solutions, and have proposed the solution that you can support with information / evidence.Begin by reading the problem statement in Step 1. Take the time to review all the information provided in the statement, including exploring the websites, videos and / or articles that are linked. Then work on steps 2 through 8 to complete this problem-based learning experience.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).

In this task students must investigate this conjecture to discover that it …

In this task students must investigate this conjecture to discover that it does not work in all cases: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.

This curriculum guide offers a list of Open Educational Resources (OER) that …

This curriculum guide offers a list of Open Educational Resources (OER) that are arranged in a logical sequence for introducing polynomials with visual models, particularly using arrays and area models.

This task looks at zeroes and factorization of a general polynomial. It …

This task looks at zeroes and factorization of a general polynomial. It is related to a very deep theorem in mathematics, the Fundamental Theorem of Algebra, which says that a polynomial of degree d always has exactly d roots, provided complex numbers are allowed as roots and provided roots are counted with the proper "multiplicity.''

The intention of this task is to provide extra depth to the …

The intention of this task is to provide extra depth to the standard A-APR.2 it is principally designed for instructional purposes only. The students may use graphing technology: the focus, however, should be on what happens to the function g when x=0 and the calculator may or may not be of help here (depending on how sophisticated it is!).

For a polynomial function p, a real number r is a root …

For a polynomial function p, a real number r is a root of p if and only if p(x) is evenly divisible by x_r. This fact leads to one of the important properties of polynomial functions: a polynomial of degree d can have at most d roots. This is the first of a sequence of problems aiming at showing this fact.

This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The …

This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The argument here generalizes, as shown in ``Zeroes and factorization of a general polynomial'' to show that a polynomial of degree d can have at most d roots. This task is intended for instructional purposes to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions.

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