Getting to Know Polynomials

Polynomials are algebraic expressions that include variables and coefficients, combined using only addition, subtraction, and multiplication. Each part separated by a plus or minus sign is called a term. The highest exponent of the variable in the polynomial is called its degree.

Structure of Polynomials

A polynomial looks like this:
\( 2x^3 - 4x^2 + 7x - 5 \)
It has four terms and a degree of 3.

Key Features

• Degree: Highest power of the variable.
• Leading Coefficient: The coefficient of the term with the highest degree.
• Constant Term: The term without a variable.

Why Polynomials Matter

Polynomials are everywhere! From calculating areas to predicting profits, polynomials help us describe and solve real-world problems.

Operations

• Adding/Subtracting: Combine like terms.
• Multiplying: Use the distributive property or special products.

Visualizing

You can graph polynomials to see their curves and how they change.

When Will You Use This?

Whether designing roller coasters or tracking the path of a ball, polynomials help model real-world scenarios.