Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. -5x^11

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients. It can include constants and can be expressed in the form of a sum of terms, where each term is a product of a coefficient and a variable raised to a power. Expressions that contain negative exponents, fractional exponents, or variables in the denominator are not considered polynomials.

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3 because the term with the highest exponent is x^3. The degree helps classify the polynomial and is crucial for understanding its behavior and graphing.

Polynomials can be classified based on the number of terms they contain. A monomial has one term (e.g., 3x), a binomial has two terms (e.g., x^2 + 4), and a trinomial has three terms (e.g., x^2 + 3x + 2). If a polynomial has more than three terms, it is simply referred to as a polynomial without a specific name. This classification aids in identifying and working with polynomials effectively.