Polynomial Evaluator (Horner Algorithm)
Local ProcessingEvaluate any polynomial P(x) = aₙxⁿ + ... + a₁x + a₀ at a specific point x using Horner's efficient method.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
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For 2x² − 3x + 1, enter "2, -3, 1" and choose x to get the value.
How to Use Polynomial Evaluator (Horner Algorithm)
- 1Enter coefficientsHighest degree first. Use 0 for missing terms (x³ − 8 → 1, 0, 0, -8).
- 2Enter xThe point to evaluate.
- 3Read the resultf(x). If it is 0, x is a root.
Examples
2x² − 3x + 1 at x = 4
Input: Coefficients 2, -3, 1 / x 4
Result: 21
x³ − 8 at x = 2
Input: Coefficients 1, 0, 0, -8 / x 2
Result: 0
Common Use Cases
- Building a table of function values
- Checking whether x is a root
- Verifying numerical analysis homework
Frequently Asked Questions (FAQ)
What if I enter coefficients in reverse?
The result changes. Always start with the highest degree.
Can coefficients be decimals?
Yes, negatives and decimals both work.