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. (3/8)x^5-(1/x^2)+9

Key Concepts

Polynomial Definition

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Each term in a polynomial is formed by multiplying a coefficient by a variable raised to a power. Expressions that include negative exponents, fractional exponents, or variables in the denominator are not considered polynomials.

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable in the expression. It provides insight into the polynomial's behavior and shape when graphed. For example, in the polynomial 3x^4 + 2x^3 - x + 5, the degree is 4, as the term with the highest exponent is x^4.

Classification of Polynomials

Polynomials can be classified based on the number of terms they contain. A monomial has one term, a binomial has two terms, and a trinomial has three terms. If a polynomial has more than three terms, it is simply referred to as a polynomial. This classification helps in understanding the structure and complexity of the polynomial.