Polynomial Calculator
Evaluate a polynomial a₃x³ + a₂x² + a₁x + a₀ at a given x. Uses Horner's method for efficient computation.
How to Use the Polynomial Calculator
- Enter the four coefficients a₀, a₁, a₂, a₃.
- Enter the value of x at which to evaluate.
- Click Evaluate to see P(x) and P'(x).
Quick Reference
| From | To |
|---|---|
| x²+2x+1 at x=3 | 16 |
| x³ at x=2 | 8 |
| 2x³−x+5 at x=1 | 6 |
| Horner's method | O(n) multiplications |
Use Cases
- •Evaluating polynomials for graphing or analysis.
- •Computing function values in numerical methods.
- •Checking polynomial homework answers quickly.
Formula
P(x) = a₃x³ + a₂x² + a₁x + a₀. Horner's form: ((a₃x + a₂)x + a₁)x + a₀. P'(x) = 3a₃x² + 2a₂x + a₁.
Frequently Asked Questions
What is Horner's method?
An efficient algorithm for evaluating polynomials that minimizes the number of multiplications.
What is the derivative?
The rate of change of the polynomial at point x. For a cubic: P'(x) = 3a₃x² + 2a₂x + a₁.
Can I enter zero coefficients?
Yes. Setting a₃ = 0 gives a quadratic; a₃ = a₂ = 0 gives a linear function.