Definitions [4]
Definition: Polynomial
A polynomial is an algebraic expression made up of terms in which the variables have non‑negative whole-number exponents.
Definition: Polynomial in One Variable
When an algebraic expression is made of only one variable, it is called a polynomial in one variable.
Examples of Polynomials in One Variable:
| Polynomial | Variable | Why it’s a polynomial |
|---|---|---|
| 3 + 5x − 7x2 | x | All exponents (0, 1, 2) are whole numbers |
| 9y3 − 5y2 + 8 | y | All exponents (3, 2, 0) are whole numbers |
| z4 + z - 1 | z | All exponents (4, 1, 0) are whole numbers |
Definition: Degree
The degree of a polynomial is simply the highest exponent (power) in the expression.
Example 1: 4x² - 3x⁵ + 8x⁶
- Term 1: 4x² → exponent = 2
- Term 2: -3x⁵ → exponent = 5
- Term 3: 8x⁶ → exponent = 6
- Degree = 6 (highest exponent)
Example 2: 25 - x⁴
- Term 1: 25 → exponent = 0 (since 25 = 25x⁰)
- Term 2: -x⁴ → exponent = 4
- Degree = 4
Definition: Degree of Polynomial
The highest power of the variable in a polynomial is called its degree.
Key Points
Key Points: General form
Quadratic polynomial
ax2 + bx + c
Cubic polynomial
ax3 + bx2 + cx + d
