  The subject matter of this work is quadratic and cubic polynomial functions
with integer coefficients;and all of whose roots are integers. The material of
this work is directed primarily at educators,students,and teachers of
mathematics,grades K12 to K20.The results of this work are expressed in
Theorems3,4,and5. Of these theorems, Theorem3, is the one that most likely, the
general reader of this article will have some familiarity with.In Theorem3,
precise coefficient conditions are given;in order that a quadratic
trinomial(with integer) have two integer roots or zeros.On the other hand,
Theorems4 and5 are largely unfamiliar territory. In Theorem4, precise
coefficient conditions are stated; for a monic cubic polynomial to have a
double(i.e.of multiplicity 2) integer root, and a single integer root(i.e.of
multiplicity 1).The entire family of such cubics can be described in terms of
four groups or subfamilies; each such group being a two-integer parameter
subfamily. In Theorem5, a one-integer parameter family of quadratic
trinomials(with integer coefficients) with two integer roots; is described.The
parameter can take any odd positive integer values.
