Question

Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial.

$2x^{-3}-4x+1$

Short answer

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

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$2x^{-3}-4x+1$.

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.