Math & Algebra Tool

Polynomial Evaluator

Evaluate a polynomial P(x) at a given x using Horner's Method.

Σ The Formula

P(x) = aₙx^n + ... + a₁x + a₀

Real World Examples

Quadratic
P(x) = x² + 2x + 1, P(2) = 9
Cubic
P(x) = 3x³ - x + 5, P(1) = 7
Linear
P(x) = 5x - 3, P(10) = 47
Constant
P(x) = 7, P(5) = 7

# About This Calculator

A Polynomial Evaluator calculates the value of a polynomial function P(x) for a specific input value of x. A polynomial is an expression consisting of variables and coefficients using addition, subtraction, and non-negative integer exponents.

For example, P(x) = 2x² + 3x - 5. To evaluate at x=2, we substitute 2 for x: 2(2)² + 3(2) - 5 = 8 + 6 - 5 = 9.

This tool uses Result's Method (Synthetic Division algorithm) under the hood, which is computationally more efficient than standard substitution, especially for higher-degree polynomials.

Useful for graphing functions, checking roots (if result is 0), and solving physics problems involving motion equations.

How To Use

  1. Enter Coefficients separated by commas, starting from the highest power (e.g., "1, 2, 1" for x²+2x+1).
  2. Enter the x value to evaluate.
  3. Click Evaluate.

Frequently Asked Questions

What format should I use for coefficients?+

List them in descending order of power. For 3x^3 - 2x + 5, you have 3x^3 + 0x^2 - 2x + 5, so enter: 3, 0, -2, 5. Don't forget zeros for missing terms!

What is Horner's Method?+

It's an algorithm for polynomial evaluation that minimizes the number of multiplications. It rewrites ax^2+bx+c as x(ax+b)+c.

What is the degree of a polynomial?+

It is the highest exponent in the expression. For x^3 + 5, the degree is 3.

What if the result is 0?+

If P(a) = 0, then 'a' is a root (or zero) of the polynomial. This means (x-a) is a factor of the polynomial.

Can I evaluate negative x values?+

Yes, simply enter a negative number for x (e.g., -5). The calculator handles sign changes correctly.

Is Polynomial Evaluator free to use?+

Yes, Polynomial Evaluator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

A Polynomial Evaluator calculates the value of a polynomial function P(x) for a specific input value of x. A polynomial is an expression consisting of variables and coefficients using addition, subtraction, and non-negative integer exponents.

For example, P(x) = 2x² + 3x - 5. To evaluate at x=2, we substitute 2 for x: 2(2)² + 3(2) - 5 = 8 + 6 - 5 = 9.

This tool uses Result's Method (Synthetic Division algorithm) under the hood, which is computationally more efficient than standard substitution, especially for higher-degree polynomials.

Useful for graphing functions, checking roots (if result is 0), and solving physics problems involving motion equations.

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