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The function given is:

\[
g(x) = \frac{6 - x^6}{5}
\]

### Step 1: Check if the function is a polynomial
A function is a polynomial if:
1. All exponents of the variable \(x\) are non-negative integers.
2. The function does not involve division by a variable (denominators must not contain variables).

In this case, \(g(x)\) is of the form \(\frac{6 - x^6}{5}\), which simplifies to:
\[
g(x) = \frac{6}{5} - \frac{1}{5}x^6
\]

This is a valid polynomial because:
- The exponents of \(x\) (specifically, 6 in \(\frac{1}{5}x^6\)) are non-negative integers.
- There is no division by a variable (the division by 5 is a constant).

### Step 2: Degree of the polynomial
The degree of a polynomial is the highest power of \(x\). In this case, the highest power of \(x\) is \(6\), so the degree of the polynomial is 6.

### Step 3: Identify the leading term and constant term
- The **leading term** is the term with the highest power of \(x\), which is \(-\frac{1}{5}x^6\).
- The **constant term** is the term without \(x\), which is \(\frac{6}{5}\).

### Answer Choices:
- **Option A** is correct: "It is a polynomial of degree **6**."

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How do you determine if a function with a fraction is a polynomial?
2. What is the general form of a polynomial?
3. Can a polynomial have negative exponents?
4. How does dividing by a constant affect whether a function is a polynomial?
5. What happens to the degree of a polynomial if all terms have the same degree?

**Tip**: The leading term of a polynomial always determines its behavior for large values of \(x\).

Determine whether the function g(x) = (6 - x^6)/5 is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

Explore how to determine if the function g(x) = (6 - x^6)/5 is a polynomial. Learn about the degree of a polynomial, identifying leading terms, and how constants affect the form. Suitable for high school students in Grades 9-12.

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