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. 9

Verified step by step guidance

1. Step 1: Understand the definition of a polynomial. A polynomial is an algebraic expression consisting of terms that are variables raised to non-negative integer exponents, combined using addition, subtraction, and multiplication by constants. There should be no variables in denominators, no negative or fractional exponents, and no variables inside functions like square roots or absolute values.
2. Step 2: Examine the given expression, which is the number 9. Since 9 is a constant term, it can be considered as a polynomial with no variable terms.
3. Step 3: Determine the degree of the polynomial. The degree of a polynomial is the highest exponent of the variable in the expression. Since 9 has no variable, its degree is 0.
4. Step 4: Classify the polynomial by the number of terms. A monomial has one term, a binomial has two terms, and a trinomial has three terms. Since 9 is a single term, it is a monomial.
5. Step 5: Conclude that the expression 9 is a polynomial, specifically a monomial of degree 0.

Key Concepts

Definition of a Polynomial

A polynomial is an algebraic expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication by non-negative integer exponents. Expressions with variables raised to negative or fractional powers, or involving division by variables, are not polynomials.

Degree of a Polynomial

The degree of a polynomial is the highest exponent of the variable in the expression. For example, in 4x^3 + 2x, the degree is 3. The degree helps classify polynomials and understand their behavior.

Classification by Number of Terms

Polynomials are classified based on the number of terms: a monomial has one term, a binomial has two terms, and a trinomial has three terms. If there are more than three terms, it is simply called a polynomial without a special name.