Question

Determine if f(x) = - (x ^ 3)/6 - 6/(x ^ 2) is a polynomial functionIf it is, and the leading coefficient . If not , state why .

Answer 1

Given function is:

$f(x)=-\frac{x^3}{6}-\frac{6}{x^2}\ldots(1)$

A polynomial is an algebraic expression that involves only positive integer exponents for the variables.

A polynomial function is of the form:

$p(x)=a_nx^n_{}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_0$

Solving equation (1)

$\begin{gathered} f(x)=-\frac{x^3}{6}-\frac{6}{x^2} \\ =-\frac{x^5+36}{6x^2} \\ =-\frac{x^{-2}(x^5+36)}{6} \end{gathered}$

We can see that the function has a negative exponent.

The given function is not a polynomial function.