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. 6x+3x^4

Verified step by step guidance

1. Step 1: Identify the expression as a polynomial or not.
2. Step 2: Check if each term in the expression is a polynomial term.
3. Step 3: Determine the degree of the polynomial.
4. Step 4: Classify the polynomial based on the number of terms.
5. Step 5: Summarize the findings.

Key Concepts

Polynomial Definition

A polynomial is a mathematical expression consisting 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 (a constant) by a variable raised to a power. For example, 3x^2 + 2x + 1 is a polynomial, while 4/x is not, as it involves division by a variable.

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 instance, in the polynomial 5x^3 + 2x^2 + 7, the degree is 3, indicating that the term with the highest exponent dominates the polynomial's behavior as x approaches infinity.

Classification of Polynomials

Polynomials can be classified based on the number of terms they contain. A monomial has one term (e.g., 4x), a binomial has two terms (e.g., x^2 + 3), and a trinomial has three terms (e.g., x^2 + 2x + 1). If a polynomial has more than three terms, it is simply referred to as a polynomial without a specific classification.