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