Determine whether the following function is a polynomial function.

Question

Determine whether the following function 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.

​F(x)=2x6−πx5+15

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Part 1

Determine whether​ F(x) is a polynomial or not. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

It is a polynomial of degree

66.

​(Type an integer or a​ fraction.)

Your answer is correct.

B.

It is not a polynomial because the variable x is raised to the

enter your response here

​power, which is not a nonnegative integer.

​(Type an integer or a​ fraction.)

C.

It is not a polynomial because the function is the ratio of two distinct​ polynomials, and the polynomial in the denominator is of positive degree.

Part 2

Write the polynomial in standard form. Then identify the leading term and the constant term. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The polynomial in standard form is

blank

with the leading term

blank and the constant

blank .

​(Use integers or fractions for any numbers in the​ expressions.)

B.

The function is not a polynomial.

Answer 1

Your answer to Part 1 is correct. This is a polynomial function with degree 6.

In Part 2, the polynomial is already in standard form, 2x⁶ - πx⁵ +15.

The leading term is 2x⁶

The constant term is 15