1.How are the concepts: indeterminate, variable, polynomial and
polynomial function defined in current secondary textbooks and are
these workable definitions?

For example, using some given definitions of
polynomial and polynomial

function (say defined over the real numbers), is it
straightforward to show:

¥*x*–1 is not a
polynomial

¥2*x *is not a polynomial function

2.How
is the arithmetic of polynomials motivated, defined and studied?

3.What are the mathematical justifications for studying
polynomials and how is the study of polynomials integrated into other areas
of

mathematics?

4.What
applications of (higher degree) polynomials are considered in high school materials?