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Expert-verified Found in: Page 430 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial.$2{x}^{-3}-4x+1$

The given expression $2{x}^{-3}-4x+1$ is not a polynomial.

See the step by step solution

## Step 1. Write the definition of the polynomial.

A monomial is a number, a variable or the product of a number and one or more variables with non-negative integer exponents. The monomial has only one term.

A polynomial is a monomial or the sum of monomials, each called a term of the polynomial.

The polynomial having only one term is called a monomial.

The polynomial having two terms is called a binomial. That is binomial is sum of two monomials.

The polynomial having three terms is called a trinomial. That is trinomial is sum of three monomials.

## Step 2. Determine whether each expression is a polynomial.

The given expression is $2{x}^{-3}-4x+1$.

It can be noticed that the first term of the given expression is the product of a number and one variable with negative integer exponents.

Therefore, the first term of the given expression is not a monomial.

As, the given expression is not sum of monomials. Therefore, the given expression is not a polynomial. ### Want to see more solutions like these? 