Let's analyze the function given in the image:

The function is: $f(x) = 2x + x^6$

Part 1: Determine if $f(x)$ is a polynomial function.

A polynomial function must have terms with variables raised to nonnegative integer powers. Here, $f(x) = 2x + x^6$ meets this criterion, since both terms have variables raised to nonnegative integer exponents (1 and 6).

Answer Choice:

• Choice B: "It is a polynomial of degree $\_\_\_\_\_$" would be correct, where we can fill in the degree.

The degree of the polynomial is determined by the highest power of $x$, which in this case is 6.

So, the correct answer here is:

• B. It is a polynomial of degree 6.

Part 2: Write the polynomial in standard form, and identify the leading term and constant term.

The standard form of a polynomial arranges the terms from the highest degree to the lowest. So, we rewrite $f(x)$ as: $f(x) = x^6 + 2x$

Now:

• The leading term is $x^6$, since it has the highest degree.
• The constant term is absent in this polynomial, as there is no term without $x$.

Answer Choice:

• Choice A in this section fits: "The polynomial in standard form is $f(x) = x^6 + 2x$ with the leading term $x^6$ and the constant 0."

Final Answers:

1. Part 1: Select B. It is a polynomial of degree 6.
2. Part 2: Select A. The polynomial in standard form is $f(x) = x^6 + 2x$ with the leading term $x^6$ and the constant 0.

Would you like further clarification on any of these steps?

Here are some related questions you may find useful:

1. What defines a polynomial function?
2. How is the degree of a polynomial determined?
3. What is the importance of the leading term in polynomials?
4. Why is it necessary to write polynomials in standard form?
5. How can you identify the constant term in a polynomial?

Tip: Remember, the degree of a polynomial is always the highest exponent of the variable in the expression when written in standard form.