Chapter A.3, Problem 26AYU

To determine

To find: Whether the expression is a polynomial. If it is, give its degree. If it is not, state why not.

Answer to Problem 26AYU

Not a polynomial; it has an exponent that is not a nonnegative integer.

Explanation of Solution

Given:

$\frac{3}{x}+2$

Calculation:

A polynomial in one variable is an algebraic expression of the form $a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0$. If $a_n\ne 0$, it is called the leading coefficient, $a_n{x}^n$ is called the leading term, and $n$ is the degree of the polynomial.

Given, $\frac{3}{x}+2=3x^{-1}+2$ is a polynomial, since it has an exponent that is not a nonnegative integer.