Polynomial Evaluator
Evaluate a polynomial at a point using Horner's method with highest-degree-first coefficients.
Description
Evaluate a polynomial at a point using Horner's method with highest-degree-first coefficients.
Evaluate a polynomial at a point using Horner's method with highest-degree-first coefficients.
When to use Polynomial Evaluator
Use this calculator for direct numerical work with the stated polynomial or equation form and for checking a hand-worked solution.
- Coefficients
- Polynomial coefficients from highest degree to constant term.
- Point
- Where to evaluate the polynomial.
How the calculation works
The formula below determines the tool output. Value: Polynomial value at x.1
p(x) = (((aₙx + aₙ₋₁)x + aₙ₋₂)x + …)x + a₀ 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
-
Horner's method — Wikipedia contributors
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