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Polynom Long Division Calculator
Ange dina polynomkoefficienter ovan och klicka på "Utför Long Division" för att se resultat.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) |
Använd det här verktyget när din divisor har en<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">x²</span>i den, eller har en ledande koefficient som inte är 1 (som<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">3x + 2</span>).
Ytterst. Verktyget injicerar automatiskt<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">0x²</span>eller<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">0x</span>platshållare i algoritmen för att hålla polynomkolumner korrekt justerade.
Eftersom du måste subtrahera hela grupperade kvantiteter. Denna miniräknare fördelar negativa tecknen felfritt.
Ja! Till skillnad från syntetisk division, hanterar polynom lång division alla divisorgrader, vilket gör det till det bästa alternativet för att dividera med kvadrater eller andra icke-linjära faktorer.
Kvoten är resultatet av divisionen (liknande hur många gånger divisorn går in i utdelningen), medan resten är vad som blir över efter att divisionen är klar.
