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.

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.