Part 1Determine 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)equals=66xplus+x cubedx3 Part 1Determine 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 not a polynomial because the variable x is raised to the [input]33 power, which is not a nonnegative integer.(Type an integer or a fraction.) B. It is a polynomial of degree [input]55 .(Type an integer or a fraction.) C. It is not a polynomial because the constant term is absent.

Question

Part 1Determine 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)equals=66xplus+x cubedx3 Part 1Determine 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 not a polynomial because the variable x is raised to the [input]33 ​power, which is not a nonnegative integer.​(Type an integer or a​ fraction.) B. It is a polynomial of degree [input]55 .​(Type an integer or a​ fraction.) C. It is not a polynomial because the constant term is absent.

BlackTom AI · Accepted Answer

The problem asks us to determine whether the given expression defines a polynomial, and if so, to state its degree, write in standard form, and identify the leading and constant terms.
First, examine the expression: f(x) = 66x + x^3. In standard polynomial form, terms are arranged from highest degree to lowest: x^3 + 66x. Each exponent on x is a nonnegative integer, and the coefficients are real numbers, so this fits the definition of a polynomial.
Regarding the degree: the highest exponent of x in the polynomial is 3 (from the term x^3). Therefore, the degree is 3.
Regarding the leading term: the leading term is the term with the highest degree, which is x^3. This is the term that dominates the polynomial for large |x| values.
Regarding the constant term: the constant term is the term independent of x. In f(x) = x^3 + 66x, there is no constant term, so the constant term is 0.
presented in standard form, the polynomial is f(x) = x^3 + 66x. Since all exponents are nonnegative integers and there is at least one term, this is indeed a polynomial.
If one were to consider potential alternative readings of the expression, such as misreading x^3 as something else, the key checks remain: exponents must be whole numbers (not fractions or negative), there must be a finite number of terms, and coefficients do not affect the classification as a polynomial as long as the exponents meet the nonnegative integer condition.
To summarize succinctly: f(x) is a polynomial of degree 3; the leading term is x^3; the constant term is 0 (absent).

Homework:Homework 8

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