This paper presents some ideas on how to utilize TI-83 Plus calculators to perform division of one polynomial (the divided) by another polynomial (the divisor) and how that procedure might be incorporated into a college algebra lesson. Four ways to obtain the quotient and remainder when dividing a polynomial by a first-degree polynomial are…

Presents a classification of factorable cubics and shows how the associated factor graphs determine domains of disconnected branches and furnish a skeletal framework for the number and shape of the branches. Illustrates three dimensional visualization and examines level curves and spikes of surfaces. (KHR)

Describes the development of a method of generating problems that are easy to present in classroom settings because all the important points to be graphed are single-digit integers. Uses an algorithm that generates intersection problems that fit the criteria. A proof of the algorithm is included. (DDR)

Develops a method for visualizing the complex roots of a polynomial equation. Illustrates some quadratic or cubic polynomials and their solutions. (KHR)

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

Presents an investigation of a third-degree polynomial using a TI-82 graphing calculator. Also includes an algebraic solution. (MKR)

The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)

Presented is a method for factoring quadratic equations that helps the teacher demonstrate how to eliminate guessing through establishment of the connection between multiplication and factoring. Included are examples that allow the student to understand the link between the algebraic and the pictorial representations of quadratic equations. (JJK)

The sign-chart method is often used to solve polynomial inequalities involving products or quotients. Presented are examples that extend this method to solve higher-degree polynomial, radical, exponential, logarithmic, absolute-value, and trigonometric inequalities and whose graphic representations lead to intuitive discussions of continuity. (MDH)

Described is an approach to the derivation of numerical integration formulas. Students develop their own formulas using polynomial interpolation and determine error estimates. The Newton-Cotes formulas and error analysis are reviewed. (KR)

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

Presents a methodology designed to strengthen the cognitive effects of using graphing calculators to solve polynomial equations using pattern matching, searching, and heuristics. Discusses pattern matching as a problem-solving strategy useful in the physical, social, political, and economic worlds of today's students. (DDR)

Discussed is how a separable field extension can play a major role in many treatments of Galois theory. The technique of diagonalizing matrices is used. Included are the introduction, the proofs, theorems, and corollaries. (KR)

Provides Terrapin LOGO programs that use graphic manipulatives--squares, logs, and units--to form the area of a rectangle as a graphical representation for any trinomial of the form: Axx + Bx + C. An important component is the connection of the procedural skill of trinomial factoring to the visualization of the accompanying rectangular displays.…

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)