Polynomial Evaluator
Evaluate polynomial p(x) = aₙxⁿ + … + a₁x + a₀ at any x. Up to degree 6.
Result
General calculation reads
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How to use this calculator
- Set non-zero coefficients (use 0 for unused terms).
- Set x value.
- Read p(x).
About this calculator
Polynomial evaluation via Horner's method: rewrite p(x) = aₙxⁿ + … + a₀ as nested multiplications: ((aₙx + aₙ₋₁)x + aₙ₋₂)x + …. Cuts the operation count from O(n²) (naive) to O(n) (linear). For p(x) = x³ − 2x² + 5x − 3 at x = 2: ((1·2 − 2)·2 + 5)·2 − 3 = ((0·2 + 5)·2 − 3) = 7. Used everywhere — graphics, signal processing, finance (NPV is a polynomial in 1/(1+r)).
Frequently asked
Why Horner's?+
Higher than degree 6?+
Real-world poly use?+
Polynomial vs. exponential growth?+
How is this different from quadratic solver?+
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