Final answer:
A polynomial is characterized by terms that contain variables and coefficients using only addition, subtraction, multiplication, and non-negative integer exponents. The algebraic expressions mentioned both qualify as polynomials because they adhere to these conditions. Simplifying these expressions by eliminating terms and checking the results maintain their polynomial nature.
Step-by-step explanation:
To determine which algebraic expressions are polynomials, we need to understand what characterizes a polynomial. A polynomial is an algebraic expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Now let's analyze the given expressions:
- 2x^3 - x^3y - 3x^2 + 6xy^2 + 5y - 2 - This expression is a polynomial because it only involves the operations mentioned above and the exponents are non-negative integers.
- -x - x^3 - x^2 + - This expression seems to be incomplete, but the part shown contains only the operations of subtraction and addition with non-negative integer exponents, and hence also forms part of a polynomial.
When we eliminate terms wherever possible to simplify the algebra, these expressions maintain their polynomial structure. Always check the answer to see if the simplifications are reasonable and that the expression still meets the criteria of a polynomial.