Polynomial evaluator
Type the coefficients from the highest power down to the constant, separated by commas, then enter x. For example 2, -3, 0, 5 means 2x³ - 3x² + 5.
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How to use it
- Enter coefficients (highest power first) and value of x.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Horner's method: start with the top coefficient, multiply by x and add the next one down to the constant, P(x) = (aₙx + aₙ₋₁)x + aₙ₋₂ and so on, with the derivative P'(x) accumulated in the same pass.
Example
Inputs: Coefficients (highest power first) = 2, -3, 0, 5, Value of x = 2. Result: P(x): 9; Degree: 3; Derivative P'(x): 12.
2, -3, 0, 5
P(x) = 2x^3 - 3x^2 + 5
Limits and caveats
- Accepts up to 30 real coefficients; write fractions as decimals, not with a slash.
- It evaluates the polynomial at x; it does not find its roots.
Questions about this tool
What do I type for a missing term?
Put 0 in its place. x³ + 1 becomes 1, 0, 0, 1.
Why Horner's method?
It needs few multiplications and additions and reduces rounding error compared with computing each power separately.
Why show the derivative?
It is the slope of the curve at x, useful for tangent lines and Newton's method.