Solucionador de equações cúbicas dedicado com raízes reais e complexas, etapas do método Cardano, gráficos cúbicos e exemplos resolvidos.
Calculadora de Divisão Longa de Polinômios
Insira seus coeficientes polinomiais acima e clique em "Execute Divisão Longa" para ver os resultados.Polynomial long division is the algebraic equivalent of numerical long division. It divides a dividend polynomial by a divisor polynomial of any degree, producing a quotient and a remainder. Unlike synthetic division, which only handles linear divisors, long division works with quadratic, cubic, or any-degree divisors.
The algorithm repeatedly: (1) divides the leading term of the current dividend by the leading term of the divisor, (2) multiplies the entire divisor by that result, (3) subtracts to get a new (reduced) dividend, and (4) repeats until the remainder's degree is less than the divisor's degree. The result satisfies Dividend = Quotient × Divisor + Remainder.
Long division is indispensable for partial fraction decomposition in calculus, for verifying that a polynomial is a factor, and for simplifying complex rational expressions. When dealing with cubic equations, it allows division by quadratic factors that arise from complex conjugate root pairs.
Decomposing rational functions for integration in calculus requires polynomial long division when the degree of the numerator exceeds the denominator.
In control engineering, simplifying transfer functions by dividing out known factors uses polynomial long division.
Confirm whether a suspected polynomial factor divides evenly into the original polynomial.
Each column must correspond to the same power of x. Skipping a degree without a zero placeholder causes cascading errors.
You subtract the product at each step. Forgetting to distribute the negative sign is the most common arithmetic mistake.
Stop when the remainder's degree is strictly less than the divisor's degree. Going further is impossible; stopping earlier is incomplete.
| Formula | P(x) = Q(x) · D(x) + R(x) |
| Divisor Degree | Any degree (not limited to linear) |
| Stops When | deg(R) < deg(D) |
| Advantage | Handles quadratic and higher divisors |
| Verification | Q(x)·D(x) + R(x) must equal P(x) |
Use esta ferramenta sempre que seu divisor tiver um<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">x²</span>nele, ou tem um coeficiente líder que não é 1 (como<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">3x + 2</span>).
Extremamente. A ferramenta injeta automaticamente<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">0x²</span>ou<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">0x</span>espaços reservados no algoritmo para manter as colunas polinomiais alinhadas corretamente.
Porque você deve subtrair quantidades inteiras agrupadas. Esta calculadora distribui os sinais negativos perfeitamente.
Sim! Ao contrário da divisão sintética, a divisão longa polinomial lida com qualquer grau divisor, tornando-a ideal para divisão por quadráticos ou outros fatores não lineares.
O quociente é o resultado da divisão (semelhante a quantas vezes o divisor vai para o dividendo), enquanto o resto é o que sobra após a conclusão da divisão.
