Identify which of the following algebraic expressions are polynomials. If so, write their degrees.
`xy+(x)/(y)-7`

Answer

To determine whether the given algebraic expression \( xy + \frac{x}{y} - 7 \) is a polynomial and to find its degree, we will analyze each term in the expression.

### Step 1: Identify the terms in the expression
The expression consists of three terms:
1. \( xy \)
2. \( \frac{x}{y} \)
3. \( -7 \)

### Step 2: Analyze each term
- **Term 1: \( xy \)**
This term can be rewritten as \( x^1y^1 \). Both \( x \) and \( y \) have positive integer powers (1), so this term is a polynomial term.

- **Term 2: \( \frac{x}{y} \)**
This term can be rewritten as \( xy^{-1} \). Here, \( y \) has a negative power (-1), which violates the property of polynomials that states all variables must have non-negative integer powers. Therefore, this term is not a polynomial term.

- **Term 3: \( -7 \)**
This is a constant term, which can be considered as \( -7x^0y^0 \). It is a polynomial term because it has non-negative integer powers.

### Step 3: Determine if the entire expression is a polynomial
Since one of the terms (\( \frac{x}{y} \)) contains a variable with a negative power, the entire expression \( xy + \frac{x}{y} - 7 \) is **not a polynomial**.

### Step 4: Conclusion
Since the expression is not a polynomial, we cannot find its degree.

### Final Answer
The expression \( xy + \frac{x}{y} - 7 \) is **not a polynomial**, and thus, it has no degree.

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