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Let's analyze the function \( h(x) = 6x^5 + 3x^3 + \frac{4}{x} \).

### Step 1: Identify the terms in the function:
- The first term is \( 6x^5 \), which is a polynomial term.
- The second term is \( 3x^3 \), which is also a polynomial term.
- The third term is \( \frac{4}{x} \), or equivalently \( 4x^{-1} \), which is not a polynomial term because it contains a negative exponent.

### Step 2: Definition of a Polynomial:
A polynomial function consists only of terms with non-negative integer exponents. Since \( \frac{4}{x} = 4x^{-1} \) contains a negative exponent, it disqualifies the entire function from being a polynomial.

### Conclusion:
The given function is **not** a polynomial. Therefore, the correct choice is:

**B. It is not a polynomial.**

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Do you have any questions or need further explanation?

Here are 5 related questions:
1. What are the key characteristics of a polynomial function?
2. How do you determine the degree of a polynomial?
3. Can a function with a fraction be a polynomial under any circumstances?
4. How does the behavior of a polynomial function change with higher-degree terms?
5. What are the differences between rational functions and polynomial functions?

**Tip:** A polynomial’s degree is determined by the highest power of \( x \) in its terms with non-negative integer exponents.

Determine whether the function h(x) = 6x^5 + 3x^3 + 4/x is a polynomial function. If it is, identify the degree.

Learn how to determine whether the function h(x) = 6x^5 + 3x^3 + 4/x is a polynomial. Understand the definition of polynomials and identify whether terms with negative exponents disqualify a function from being a polynomial. Suitable for high school students in Grades 9-12.

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