Polynomial Operations
Perform polynomial algebra: add, subtract, multiply, divide (with quotient and remainder), scalar-multiply, evaluate, differentiate, integrate, and find the greatest common divisor. Enter two polynomials in standard algebraic form (e.g. x^3 - 2x^2 + 3x - 5, 2x + 1, or 4), pick an operation, and see the simplified result. Everything runs locally in your browser.
Result
A polynomial is a sum of terms aₙxⁿ. This tool keeps polynomials in coefficient form and performs exact arithmetic on them: add/subtract combine like terms, multiply convolves coefficients, divide uses polynomial long division to produce a quotient and remainder (A = Q·B + R, with deg R < deg B), evaluate uses Horner's method, differentiate applies the power rule termwise, integrate adds one to each exponent and divides by the new exponent, and gcd runs the Euclidean algorithm (returned monic). Enter polynomials like x^2 + 2x + 1, -x^3 + 4, or 3; decimals like 1.5x^2 are fine. Pairs with the Polynomial Interpolation and Matrix Calculator tools. Everything runs locally — nothing leaves your browser.