Pemecah persamaan kubik khusus dengan akar nyata dan kompleks, langkah-langkah metode Cardano, grafik kubik, dan contoh kerja.
Kalkulator Pembagian Panjang Polinomial
Masukkan koefisien polinomial Anda di atas dan klik "Lakukan Divisi Panjang" untuk melihat hasilnya.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) |
Gunakan alat ini setiap kali pembagi Anda memiliki<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">x²</span>di dalamnya, atau memiliki koefisien utama yang bukan 1 (seperti<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">3x + 2</span>).
Sangat. Alat ini secara otomatis menyuntikkan<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">0x²</span>atau<span class="font-mono text-primary-700 bg-primary-50 px-1 rounded">0x</span>placeholder ke dalam algoritme untuk menjaga kolom polinomial tetap sejajar dengan benar.
Karena Anda harus mengurangkan seluruh besaran yang dikelompokkan. Kalkulator ini mendistribusikan tanda-tanda negatif dengan sempurna.
Ya! Tidak seperti pembagian sintetik, pembagian panjang polinomial menangani derajat pembagi apa pun, menjadikannya pilihan yang tepat untuk membagi dengan kuadrat atau faktor nonlinier lainnya.
Hasil bagi adalah hasil pembagian (sama dengan berapa kali pembagi menjadi pembagian), sedangkan sisanya adalah sisa setelah pembagian selesai.
