Identify which of the following expressions are polynomials. If so, write their degrees.
`5x^(2)-(2)/(x)+7`

Answer

To determine whether the expression \(5x^2 - \frac{2}{x} + 7\) is a polynomial and to find its degree, we will follow these steps:

### Step 1: Identify the terms in the expression
The given expression is:
\[ 5x^2 - \frac{2}{x} + 7 \]

This expression consists of three terms:
1. \(5x^2\)
2. \(-\frac{2}{x}\)
3. \(7\)

### Step 2: Rewrite the expression
We can rewrite \(-\frac{2}{x}\) as \(-2x^{-1}\). So the expression can be rewritten as:
\[ 5x^2 - 2x^{-1} + 7 \]

### Step 3: Check the powers of the variable
Now, let's check the powers of \(x\) in each term:
1. In \(5x^2\), the power of \(x\) is \(2\).
2. In \(-2x^{-1}\), the power of \(x\) is \(-1\).
3. In \(7\), there is no \(x\), which can be considered as \(x^0\) (power \(0\)).

### Step 4: Determine if the expression is a polynomial
A polynomial is defined as an expression that consists of terms with non-negative integer powers of the variable. Since the term \(-2x^{-1}\) has a negative power, this expression is **not a polynomial**.

### Step 5: Conclusion
Since one of the terms has a negative power, the expression \(5x^2 - \frac{2}{x} + 7\) is not a polynomial.

### Summary
- The expression is **not a polynomial** because it contains a term with a negative exponent.

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