Basic Concepts
In a nutshell: Polynomials are algebraic expressions made up of terms with variables raised to whole number exponents.
## 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.
Examples
- Adding \( (2x^2 + 3x) + (x^2 - x) = 3x^2 + 2x \)
- Multiplying \( (x + 2)(x - 3) = x^2 - x - 6 \)
Key terms
- Polynomial
- An expression made of terms with variables raised to non-negative integer exponents.
- Degree
- The highest exponent in the polynomial.
- Leading Coefficient
- The coefficient of the highest degree term.