## Precalculus (10th Edition)

Published by Pearson

# Appendix A - Review - A.3 Polynomials - A.3 Assess Your Understanding - Page A30: 29

#### Answer

Not a polynomial, because not all terms in the sum are monomials. (The variable has a negative exponent in one of the terms)

#### Work Step by Step

A monomial is an expression of the form $ax^{k}$, where $x$ is the variable, the exponent $k$, a nonnegative integer, is the degree, and $a$ is the coefficient of the term. A polynomial expression is either a single monomial or a SUM of several monomials. The degree of the polynomial is the degree of the monomial with the highest degree. Here, we have $3x^{2}-\displaystyle \frac{5}{x}=3x^{2}-5x^{-1}$ The second term is not a monomial, because the variable has a negative exponent. So, the expression is not a polynomial. Not a polynomial, because not all terms in the sum are monomials. (The variable has a negative exponent in one of the terms).

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