Final answer:
Options 1) 2x + 3 and 2) 3x² + 4x - 1 are polynomials as they consist of variables raised to non-negative integer exponents and do not have variables in the denominator or under a square root.
Step-by-step explanation:
The student is asking which of the provided options represents a polynomial. By definition, a polynomial is an expression consisting of variables (also called indeterminates), coefficients, and non-negative integer exponents of the variables. It may contain several terms, which are the products of a number and a variable raised to an exponent.
Looking at the options given: 1) 2x + 3 is a polynomial as it has terms with variables raised to non-negative integer exponents; 2) 3x² + 4x - 1 is also a polynomial; 3) 5/x is not a polynomial because it contains a variable in the denominator; and 4) √x is not a polynomial because the variable x is under a square root, which is equivalent to an exponent of 1/2, not an integer.
Therefore, the main answer to the student's question is that both options 1) 2x + 3 and 2) 3x² + 4x - 1 represent polynomials.