4.1 Classifying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What are the different classifications of polynomials based on the number of terms?

Back

Polynomials can be classified as monomials (1 term), binomials (2 terms), trinomials (3 terms), and polynomials (4 or more terms).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term's degree and its coefficient. It describes how the function behaves as x approaches positive or negative infinity.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

The end behavior will be both ends of the graph rising to positive infinity (∞, ∞).

Front

What is the end behavior of a polynomial with an even degree and a negative leading coefficient?

Back

The end behavior will be both ends of the graph falling to negative infinity (-∞, -∞).

Front

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

Back

The end behavior will be the left end falling to negative infinity and the right end rising to positive infinity (-∞, ∞).

Front

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

Back

The end behavior will be the left end rising to positive infinity and the right end falling to negative infinity (∞, -∞).

Front

How do you classify the polynomial 3x⁴ + 14x³ − 2x²?

Back

This polynomial is classified as a trinomial because it has three terms.

Front

How do you classify the polynomial 6x³ + 3x² + 2x − 4?

Back

This polynomial is classified as a polynomial because it has four terms.