Calculadora de Divisão Sintética (por x − r)

The synthetic division calculator is a practical tool for performing polynomial division using the Briot-Ruffini method, specifically for divisors of the form (x − r). It accepts a degree-2 polynomial (a₂x² + a₁x + a₀) and a real value r, returning the quotient and remainder. The process is faster than traditional long division.

The algorithm works by arranging the polynomial coefficients (a₂, a₁, a₀) in a row and performing successive additions and multiplications with the value r below. The result is a degree-1 quotient (b₁x + b₀) and a constant remainder. For example, dividing 2x² + 3x + 1 by (x − 1) yields quotient 2x + 5 and remainder 6.

Use this calculator when you need to quickly check if (x − r) is a factor of the polynomial (remainder zero) or to simplify algebraic expressions. It is useful in algebra homework, root finding, and engineering problems involving polynomials. Synthetic division is a standard method in calculus and linear algebra courses.

Caution: ensure the polynomial is in standard form (descending degree) and that all terms, including those with zero coefficients, are included. The divisor must be exactly (x − r); for divisors like (x + 2), use r = −2. The method applies only to linear divisors. Verify that the coefficients are real numbers.