Which one is polynomial ?

Options

A. `(1)/(x+1)`
B. `sqrtx+2`
C. `(1)/(x^(2)+2x+7)`
D. `x^(3)+1`

Explanation

To determine which expression is a polynomial, we need to understand the definition of a polynomial. A polynomial is an expression that consists of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication.

Let's analyze the given options step by step:

1. **Identify the Expressions**: We need to look at the expressions provided in the question (not given here, but we will assume there are multiple expressions to evaluate).

2. **Check for Variables and Coefficients**: For each expression, identify the variables and their coefficients. A variable is typically represented by letters (like x, y, etc.), and the coefficient is the number that multiplies the variable.

3. **Examine the Powers of Variables**: Check the powers (exponents) of the variables in each expression. The powers must be non-negative integers (0, 1, 2, 3, ...).

4. **Look for Operations**: The operations allowed in a polynomial are addition (+), subtraction (-), and multiplication (×). Division or negative powers of variables disqualify an expression from being a polynomial.

5. **Evaluate Each Expression**:
- If any expression contains division by a variable (e.g., 1/x), it is not a polynomial.
- If any expression has a variable raised to a negative power (e.g., x^(-1)), it is not a polynomial.
- If all variables have non-negative integer powers and the operations are limited to addition, subtraction, and multiplication, then it is a polynomial.

6. **Identify the Polynomial**: After evaluating all expressions, identify which one meets the criteria for being a polynomial.

**Conclusion**: Based on the analysis, the expression that meets all the criteria of a polynomial is the correct answer.