Evaluate a polynomial from descending-order coefficients at a chosen x value. The calculation trail makes the reported polynomial value easier to reproduce.
A coefficient list [aₙ,…,a₀] represents aₙxⁿ+…+a₀. Horner’s method nests the expression to reduce the number of multiplications.
Check Polynomial from Coefficients, highest power first, then verify Value of x. Estimate the Polynomial Polynomial value before computing it again. If Value of x changes during Polynomial, keep Value of x fixed. That Polynomial comparison shows whether Polynomial value moves as expected.
Evaluation tests roots, fills function tables, supports interpolation, and checks polynomial identities numerically.
Zero coefficients must remain in the list to preserve missing powers. Coefficients are entered from highest degree to constant term. If the Polynomial Evaluator assumptions do not fit, consider multiply polynomials.
Start with the leading coefficient, repeatedly multiply the running result by x, and add the next coefficient.
Coefficients 2,−3,0,5 represent 2x³−3x²+5. At x=4, Horner’s method gives 85. This Polynomial Evaluator example can be compared with add polynomials.
The polynomial 2x³−3x²+5 can be nested as ((2x−3)x+0)x+5. Reading coefficients in order makes the missing x term visible as zero. Evaluating both the expanded and nested forms at a simple value supplies an independent check on coefficient order.
Substitute the Polynomial solution into Coefficients, highest power first. This Polynomial check rejects false Polynomial branches and forbidden denominators.
Choose an easy Coefficients, highest power first value before running Polynomial. Predict Value of x, then compare it with the Polynomial output.
Choose a nearby Coefficients, highest power first whose effect on Polynomial value is easy to anticipate. With Value of x held constant, the Polynomial result should move in the expected direction. This controlled Polynomial comparison is more revealing than several simultaneous edits.
Units and conventions belong with a Polynomial answer. Confirm that Coefficients, highest power first and Value of x use the intended interpretation, then label Polynomial value the same way. A numerically correct Polynomial value can still answer the wrong Polynomial question when that context changes.
They hold the place of missing powers.
Highest power first.
A nested evaluation requiring fewer operations.
Yes.