Question

determine if f(x)=2x^3+20^2-1/x is a polynomial function. if it is, state the degree and the leading coefficient. if not, state whyNo. The leading coefficient is not a whole number.Yes. The degree is 2 and the leading coefficient is 3.Yes. The degree is 3 and the leading coefficient is 2.No. There is an exponent on a variable x that is not a whole number.

Answer 1

The given function is:

`f(x)=2x^3+2x^2-(1)/(x)`

The last term of the function can be expressed as:

`\begin{gathered} (1)/(x)=x^(-1) \\ \text{ So:} \\ f(x)=2x^3+2x^2-x^(-1) \end{gathered}`

By definition, a polynomial function consists of:

As we can observe, the last term is raised to a negative integer power, -1 is not a whole number. Then this is not a polynomial function.

The answer is: No. There is an exponent on a variable x that is not a whole number. (the last option)