Understanding Polynomials
Polynomials are algebraic expressions that consist of variables and coefficients, combined using addition, subtraction, and multiplication. They are characterized by their degree, which is the highest power of the variable in the expression.
Types of Polynomials
- Monomial: A polynomial with one term (e.g., 4x).
- Binomial: A polynomial with two terms (e.g., 3x + 2).
- Trinomial: A polynomial with three terms (e.g., x² + 2x + 1).
Test for Polynomial
To determine if an expression is a polynomial, check the following criteria:
- Non-negative Integer Exponents:
- All exponents of the variables must be whole numbers (0, 1, 2, ...).
- No Division by Variables:
- The expression must not have variables in the denominator.
- No Negative Exponents:
- Ensure that no term has a variable raised to a negative exponent.
Examples of Polynomials
- 3x² + 2x + 1 (This is a polynomial.)
- x⁻² + 5 (This is not a polynomial due to the negative exponent.)
- 1/(x + 1) (This is not a polynomial due to division by a variable.)
Importance of Polynomials
Polynomials are fundamental in algebra and calculus. They are used in various applications including:
- Modeling real-world scenarios
- Solving equations
- Graphing functions
Resources for Further Study
Explore various resources such as notes, videos, and practice tests available on EduRev to deepen your understanding of polynomials and their applications in mathematics.

Https://edurev.page.link/h8f8srgrUfE7fJ5B7