Question

Hello good morning May I get some help with this question?

Answer 1

SOLUTION

We want to check if the following is a polynomial

$f(x)=6-\frac{5}{x^5}$

Now, let us write the function in standard form

$\begin{gathered} f(x)=6-\frac{5}{x^5} \\ f(x)=6-5\times\frac{1}{x^5} \\ f(x)=6-5\times x^{-5} \\ f(x)=6-5x^{-5} \end{gathered}$

Hence, the function in standard form is

$f(x)=-5x^{-5}+6$

The function is not a polynomial because it has an x raise to a negative number. Polynomials should have positive powers.

The leading term of the polynomial is

$-5x^{-5}$

The constant term is 6