Determine whether each expression is a polynomial. If the...

Determine whether each expression is a polynomial. If the polynomial has a specific name, for example, "monomial" or "binomial," give the name. If the expression is not a polynomial, explain why it is not.$5 z^{-3}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Polynomial Definition

A polynomial is an expression that consists of variables and coefficients, constructed using the operations of addition, subtraction, and multiplication, where every term’s variable is raised to a non-negative integer exponent. This definition ensures that the function is defined for all real numbers and facilitates algebraic operations such as addition and factoring.

Monomial

A monomial is a specific type of polynomial that contains only one term, where this term is a product of a constant and a variable raised to a non-negative integer exponent. Monomials are the simplest building blocks of polynomials, and their structure adheres strictly to the rules of polynomials.

Negative Exponents

Negative exponents indicate reciprocal relationships rather than multiplication by a variable raised to a positive power. In the context of polynomials, the exponents must be non-negative integers; therefore, any term with a negative exponent does not meet the criteria and disqualifies the expression from being considered a polynomial.

Please give Ace some feedback