Examples
Examples
Try the starting example
- Dividend coefficients, highest degree first
- 1,-3,2
- Divisor coefficients, highest degree first
- 1,-1
- Reconstruction check x
- 3
- Quotient coefficients, highest degree first
- 1, -2
- Remainder coefficients
- 0
- Dividend at check x
- 2
- Reconstructed value at check x
- 2
- Absolute reconstruction difference
- 0
Try another scenario
- Dividend coefficients, highest degree first
- 1,0,0,2
- Divisor coefficients, highest degree first
- 1,1
- Reconstruction check x
- 3
- Quotient coefficients, highest degree first
- 1, -1, 1
- Remainder coefficients
- 1
- Dividend at check x
- 29
- Reconstructed value at check x
- 29
- Absolute reconstruction difference
- 0
Calculation method
Calculation method
Quotient coefficients, highest degree first
Polynomial long division: eliminate the next leading dividend term using the divisor leading coefficient.
Remainder coefficients
Terms below the divisor degree left after elimination; the zero remainder is represented by 0.
Dividend at check x
Horner evaluation of the entered dividend.
Reconstructed value at check x
Quotient(x)×divisor(x)+remainder(x).
Absolute reconstruction difference
Absolute difference between the two evaluations.
Symbols and units
- a
- Dividend coefficients, highest degree first
- b
- Divisor coefficients, highest degree first
- c
- Reconstruction check x
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Finite real coefficients with up to 30 coefficients in each polynomial. The divisor leading coefficient must be nonzero; coefficient outputs keep their algebraic descending order. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: polynomial long division ↗
Background reading; this does not imply endorsement or independent review of SumFizz.