After several such examples, the students should be asked to explore ways to find the final

trinomial answer to the product without writing out the steps of the distributive property.

More recently, Feurzeig, Katz, Lewis, and Steinbock (2000a, 2000b) proposed computer-based representations of properties of monic quadratic

trinomials in the plane of their coefficients (parameters).

The range of subtopics included: expanding three factors, expanding the difference between two squares, and factorising quadratic

trinomials. The students were given two weeks to clarify the task, and learn and understand the topic with assistance by the teacher.

Bonnie seemed to have some competence performing basic skills such as factoring

trinomials and solving first and second degree equations, yet lacked confidence for more complex problems.

Tzekaki); (13) Students' Beliefs and Attitudes about Studying and Learning Mathematics (Eleftherios Kapetanas and Theodosios Zachariades); (14) "How Can We Describe the Relation between the Factored Form and the Expanded Form of These

Trinomials? We Don't even Know If Our Paper-and-Pencil Factorizations are Right": The Case for Computer Algebra Systems (CAS) with Weaker Algebra Students (Carolyn Kieran and Caroline Damboise); (15) What Is a Beautiful Problem?

After reviewing the arithmetic of whole numbers, this textbook introduces fractions, decimals, percents, and basic geometry, then explains the operations of functions, exponents, polynomials, rational expressions, radicals, factoring

trinomials, and solving systems of equations.

in this experiment we chose four primitive

trinomials, f(D) = D.sup.31.

Emphasizing reasoning skills, this textbook introduces techniques for solving algebraic equations, graphing linear equations, adding and subtracting polynomials and rational expressions, factoring

trinomials, and solving systems of equations.

Wu [7] has chosen a new Montgomery factor and shown that choosing the middle term of the irreducible

trinomial G([omega])= [[omega].sup.m] + [[omega].sup.k] + 1 as the Montgomery factor, i.e., R=[x.sup.k], results in more efficient bit-parallel architectures.

Another interesting special case in terms of implementation is when the characteristic polynomial f(x) is only a

trinomial, of the form f(x) = [x.sup.k] [a.sub.1.X.sup.k-1] - [a.sub.k], for 1 [is less than or equal to] j [is less than] k.