What type of polynomial is #2y^2 + 6y^5 z^3#?

1 Answer
Jun 20, 2015

It is an 8th degree polynomial over the integers in two variables.


It is obvious that there are two variable, which explains the phrase "in two variables".

The degree of a term (with non-zero coefficient) is the sum of the exponents on the variables, so the term #2y^2# is degree 2, and the term #6y^5z^3# is degree 8.
The degree of a polynomial is the maximum of the degrees of its term with non-zero coefficients.
Therefore the example has degree #8#.

The coefficients are integers, so it is a polynomial "over the integers" .
(Since the coefficients are, in fact, whole, or even natural numbers we could say it is a polynomial over the whole or natural numbers, but it is rare to leave out the negatives for polynomials.)

Since the integers are included in the rational numbers, the real numbers and the complex numbers, we could also consider this a polynomial over those sets.

A longer phrase use is "polynomial with integer coefficients". It is more informative, but longer than the phrase used above.