Calculadora de Divisão de Polinômios (por x − r)

The Polynomial Division Calculator (by x − r) performs the division of a second-degree polynomial P(x) = a₂x² + a₁x + a₀ by the binomial (x − r) using the Briot-Ruffini algorithm. The result shows the quotient Q(x) (a first-degree polynomial) and the remainder. This tool is ideal for students and professionals who need to quickly verify this type of algebraic operation.

The Briot-Ruffini algorithm is an efficient method for dividing polynomials by binomials of the form (x − r). It uses a table with the coefficients of the dividend and the root r, performing successive additions and multiplications. The final result provides the coefficients of the quotient and the remainder value, which is a real number. The calculator automates the entire process, avoiding manual errors.

Use this calculator when you need to find the quotient and remainder of dividing a quadratic polynomial by (x − r). It is useful in contexts such as polynomial factoring, solving equations, simplifying expressions, and applying the Remainder Theorem. For example, to check if a number is a root of a polynomial, a remainder of zero indicates that (x − r) is a factor.

Caution: Ensure you enter the coefficients correctly, including negative signs. The polynomial must be in standard form a₂x² + a₁x + a₀. This calculator is not suitable for higher-degree polynomials. Also, remember that the Briot-Ruffini method only applies to linear divisors of the form (x − r).