Questions: 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)=4 x^6-π x^4+1/2 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 . (Type an integer or a fraction.) B. It is not a polynomial because the variable x is raised to the (Type an integer or a fraction.) power, which is not a nonnegative integer. 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. 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 F(x)= with the leading term (Use integers or fractions for any numbers in the expressions.) and the constant . B. The function is not a polynomial.

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)=4 x^6-π x^4+1/2 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 . (Type an integer or a fraction.) B. It is not a polynomial because the variable x is raised to the (Type an integer or a fraction.) power, which is not a nonnegative integer. 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. 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 F(x)= with the leading term (Use integers or fractions for any numbers in the expressions.) and the constant . B. The function is not a polynomial.
Transcript text: 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. \[ F(x)=4 x^{6}-\pi x^{4}+\frac{1}{2} \] 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 $\square$ . (Type an integer or a fraction.) B. It is not a polynomial because the variable $x$ is raised to the (Type an integer or a fraction.) $\square$ power, which is not a nonnegative integer. 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. 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 $F(x)=$ $\square$ with the leading term (Use integers or fractions for any numbers in the expressions.) $\square$ and the constant $\square$ . B. The function is not a polynomial. Next
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Solution

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Solution Steps

Step 1: Check for Polynomial Criteria

All terms have non-negative integer powers and real number coefficients, so it is a polynomial.

Step 2: Determine Degree

The degree of the polynomial is 6.

Step 3: Standard Form

The polynomial in standard form is: \( 0.5 - 3.141592653589793x^4 + 4x^6 \).

Step 4: Identify Leading and Constant Terms

The leading term is 4 with a degree of 6, and the constant term is 0.5.

Final Answer:

The given function is a polynomial of degree 6, in standard form it is \( 0.5 - 3.141592653589793x^4 + 4x^6 \), with a leading term coefficient of 4 and a constant term of 0.5.

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