What is a Polynomial?
A polynomial is an expression consisting of constants and variables. The only operations used in a polynomial function are addition, subtraction, multiplication, and exponentiation.
Types of Polynomials
The type of polynomial is determined by the number of terms in an expression.
| Number of Terms | Polynomial Name | Example |
|---|---|---|
| 1 | Monomial | 5x² |
| 2 | Binomial | 3x + 2 |
| 3 | Trinomial | x² + 4x + 3 |
| 4 | Quadrinomial | x³ + 2x² + 5x + 7 |
| 5+ | Polynomial | x⁴ + 3x³ + 2x² + x + 6 |
Degree of a Polynomial
The degree of a polynomial is determined by the highest exponent on a variable.
| Degree of Polynomial | Degree Name | Example |
|---|---|---|
| 0 | Constant | 5 |
| 1 | Linear | 3x + 2 |
| 2 | Quadratic | x² + 4x + 3 |
| 3 | Cubic | x³ + 2x² + 5 |
| 4 | Quartic | x⁴ + x³ + x² + x + 1 |
Naming a Polynomial
Naming a polynomial is simple: it's a combination of the degree name with the polynomial type.
Examples:
- Quadratic Binomial: x² + 3x + 1
- Cubic Trinomial: x³ + 4x² + x
- Quartic Polynomial: x⁴ + 2x³ + 5x² + 7x + 3
- Cubic Quadrinomial: x³ + x² + x + 1
Test Your Knowledge
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