Polynomial Evaluator
Evaluate polynomial p(x) = aₙxⁿ + … + a₁x + a₀ at any x. Up to degree 6.
Result
p(2)
7.000000
Polynomial: x^3 - 2x^2 + 5x - 3.
- Polynomialx^3 - 2x^2 + 5x - 3
- Degree3
- x2
- p(x)7.00000000
- Horner 10 = 0.0000.
- Horner 2prev × 2 + 0 = 0.0000.
- Horner 3prev × 2 + 0 = 0.0000.
- Horner 4prev × 2 + 1 = 1.0000.
- Horner 5prev × 2 + -2 = 0.0000.
Step-by-step
- Use Horner's method: ((((a₆x + a₅)x + a₄)x + a₃)x + a₂)x + a₁)x + a₀.
- Step 1: 0 = 0.0000.
- Step 2: prev × 2 + 0 = 0.0000.
- Step 3: prev × 2 + 0 = 0.0000.
- Step 4: prev × 2 + 1 = 1.0000.
- Step 5: prev × 2 + -2 = 0.0000.
- Step 6: prev × 2 + 5 = 5.0000.
- Step 7: prev × 2 + -3 = 7.0000.
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
Fewer multiplications, fewer rounding errors, and O(n) work vs. O(n²) naive. The standard polynomial evaluation algorithm.
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