Polynomial Classification

Definition of Polynomial:
A polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Binomial, Trinomial, and Polynomial:
- Binomial: A binomial is a polynomial with exactly two terms. For example, x + y is a binomial.
- Trinomial: A trinomial is a polynomial with exactly three terms. For example, x^2 + 2x + 1 is a trinomial.
- Polynomial: A polynomial can have any number of terms. It can be a binomial, trinomial, or have even more terms. For example, 3x^3 + 2x^2 - 5x + 7 is a polynomial.

Analysis of the Given Expression:
The given expression is Xyz × xz, x + 3xy - 1.
- The expression Xyz × xz can be simplified to X^2 yz^2.
- The expression x + 3xy - 1 is already in its simplified form.

Final Classification:
The given expression X^2 yz^2 + x + 3xy - 1 is a polynomial because it consists of multiple terms involving variables and coefficients, and includes the operations of addition and multiplication. Therefore, it is not a binomial or trinomial, but a polynomial.
Therefore, the expression X^2 yz^2 + x + 3xy - 1 is a polynomial.