How to Use the Polynomial Calculator

Enter two polynomials using either standard notation (like 3x^2 + 2x - 1) or comma-separated coefficients (like -1, 2, 3 for the same polynomial). Select the operation you want to perform and click Calculate.

Input Formats

The calculator accepts polynomials in two formats:

Standard Form: Use x for the variable and ^ for exponents (e.g., 3x^2 + 2x - 1)
Coefficient Form: List coefficients from constant term to highest power, separated by commas (e.g., -1, 2, 3)

Polynomial Operations

Addition

To add polynomials, combine like terms (terms with the same power of x). For example: (3x² + 2x - 1) + (x² - 4x + 5) = 4x² - 2x + 4

Subtraction

To subtract polynomials, distribute the negative sign and combine like terms. For example: (3x² + 2x - 1) - (x² - 4x + 5) = 2x² + 6x - 6

Multiplication

To multiply polynomials, use the distributive property (FOIL for binomials). Each term in the first polynomial multiplies each term in the second, then combine like terms.

Key Polynomial Terms

Degree: The highest power of x with a non-zero coefficient
Leading Coefficient: The coefficient of the highest-degree term
Constant Term: The term with no x (power of 0)
Like Terms: Terms with the same power of x

Common Applications

Polynomial arithmetic is fundamental in:

Algebra and precalculus courses
Engineering and physics calculations
Computer graphics and animation
Signal processing and control systems
Cryptography and coding theory