Introduction
A polynomial in one variable is an algebraic expression that contains only one variable.
Example: p(x) = 2x² + 5x - 3 (Variable is x).
Example: q(y) = y³ - 1 (Variable is y).
Standard Form
an xⁿ + an-1 xⁿ⁻¹ + ... + a1x + a0
Where an, an-1, ..., a0 are constants and an ≠ 0.
Degree of a Polynomial
The highest power of the variable in a polynomial is called the degree of the
polynomial.
Example: In 4x³ - 2x² + 8x - 1, the highest power is 3. So, degree = 3.
Classification based on Degree
- Linear Polynomial: A polynomial of degree 1. (e.g., 2x + 1)
- Quadratic Polynomial: A polynomial of degree 2. (e.g., x² - 4)
- Cubic Polynomial: A polynomial of degree 3. (e.g., x³ + 2x² - x + 1)
Classification based on Terms
- Monomial: Polynomial with 1 term. (e.g., 2x)
- Binomial: Polynomial with 2 terms. (e.g., x + 1)
- Trinomial: Polynomial with 3 terms. (e.g., x² + x + 1)