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Cubic by Quadratic Polynomial Division Calculator — result sheet
Divide a cubic polynomial by a quadratic polynomial and return the linear quotient, linear remainder, and an identity check.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For D(x)=a₃x³+a₂x²+a₁x+a₀ and d(x)=b₂x²+b₁x+b₀ with b₂≠0, q₁=a₃/b₂, q₀=(a₂−q₁b₁)/b₂, r₁=a₁−(q₁b₀+q₀b₁), and r₀=a₀−q₀b₀; D = dq + r.
This is a deliberately bounded long-division contract: a degree-three dividend and degree-two divisor produce a linear quotient and a remainder of degree at most one. Keeping the coefficients visible makes it possible to multiply the divisor and quotient and check the remainder instead of treating polynomial division as a black-box text parser.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Dividend x³ coefficient — minimum -1000000; maximum 1000000
- Dividend x² coefficient — minimum -1000000; maximum 1000000
- Dividend x coefficient — minimum -1000000; maximum 1000000
- Dividend constant — minimum -1000000; maximum 1000000
- Divisor x² coefficient — minimum -1000000; maximum 1000000
- Divisor x coefficient — minimum -1000000; maximum 1000000
- Divisor constant — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Dividend x³ coefficient | 2 |
| Dividend x² coefficient | -3 |
| Dividend x coefficient | 4 |
| Dividend constant | 5 |
| Divisor x² coefficient | 1 |
| Divisor x coefficient | -1 |
| Divisor constant | 1 |
(2x³−3x²+4x+5)/(x²−x+1) = 2x−1 + (x+6)/(x²−x+1).
Assumptions and limits
- The dividend is represented by four coefficients from x³ through the constant term.
- The divisor is represented by three coefficients from x² through the constant term and its leading coefficient must be nonzero.
- Missing powers are represented by zero coefficients rather than omitted fields.
- The result uses real floating-point coefficients and reports an identity residual for D−(dq+r).
- The page does not factor either polynomial or find roots.
- It does not parse symbolic expressions, coefficients with units, or divisors of degree three or higher.
- Rounding is applied to display only; keep the coefficient convention with any copied result.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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