Synthetic Division Calculator
Divide a polynomial (highest-degree-first coefficients) by (x - r) using synthetic division, returning the quotient and remainder.
Description
Divide a polynomial (highest-degree-first coefficients) by (x - r) using synthetic division, returning the quotient and remainder.
Divide a polynomial (highest-degree-first coefficients) by (x - r) using synthetic division, returning the quotient and remainder.
When to use Synthetic Division Calculator
Use this calculator for direct numerical work with the stated polynomial or equation form and for checking a hand-worked solution.
- Dividend coefficients
- Dividend coefficients from highest degree to constant term.
- Divisor root
- Root r of the linear divisor (x - r).
How the calculation works
The formula below determines the tool output. Quotient coefficients: Quotient coefficients from highest degree to constant term. Remainder: Remainder of the division.1
p(x) = (x − r)q(x) + p(r) Limitations and assumptions
Coefficients are evaluated with floating-point arithmetic. Ill-conditioned systems, nearly repeated roots, and coefficients with very different magnitudes can magnify representation error; the result is not a symbolic proof.
Alternative or Complementary approaches
Complement the numerical result by substituting it back into the original expression. Symbolic algebra or higher-precision arithmetic is a better alternative when an exact form or a proof is required.
References
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Synthetic division — Wikipedia contributors
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