Determine whether the function is a polynomial function. If it is, identify the degree. $$ g(x)=2 x^{7}-\pi x^{4}+\frac{1}{7} x^{3} $$ Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It is a polynomial. The degree of the polynomial is B. It is not a polynomial.

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We start by noting that a polynomial function is any function of the form

$$
p(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0,
$$

where the coefficients $$a_n, a_{n-1}, \dots, a_0$$ are real numbers, and $$n$$ is a nonnegative integer.

The given function is

$$
g(x)=2 x^{7}-\pi x^{4}+\frac{1}{7} x^{3}.
$$

Each term in $$g(x)$$ is of the form $$a x^n$$ where the exponents $$7$$, $$4$$, and $$3$$ are nonnegative integers, and the coefficients $$2$$, $$-\pi$$, and $$\frac{1}{7}$$ are real numbers. Therefore, $$g(x)$$ is a polynomial.

Now, the degree of a polynomial is the highest exponent of $$x$$ that appears in the polynomial with a nonzero coefficient. Here, the highest exponent is $$7$$.

Thus, the function $$g(x)$$ is a polynomial function of degree $$7$$.

A. It is a polynomial. The degree of the polynomial is 7.
A. It is a polynomial. The degree of the polynomial is 7.

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