Polynomial Evaluator

Enter coefficients from highest power to constant and an x value to calculate P(x).

Stable numericsSubstitute / reconstructIndependent checkLocal calculation

Coefficients, highest power first

P(2) = 72x^3 - 3x^2 + 4x - 5

Horner steps, derivative value & evaluation table

Reuse the coefficient list and x above. Horner's method evaluates the polynomial with one multiply-and-add per coefficient; the same pass also exposes the synthetic-division remainder P(x).

Additional x valuesDisplayed significant digits

—Degree

—P′(x)

—Remainder ÷ (x − current x)

—Derivative polynomial

Numeric evaluation uses JavaScript floating-point arithmetic; very ill-conditioned coefficients can still require higher-precision software.