Calculator Form
Example Data Table
| Scenario | Polynomial A | Polynomial B | Operation | Example Output |
|---|---|---|---|---|
| Combine like terms | 4x^3 - 2x + 5 | — | Simplify | 4x^3 - 2x + 5 |
| Evaluate at x = 2 | x^3 - 4x + 1 | — | Evaluate | 1 |
| Polynomial sum | 2x^2 + 3x - 1 | x^2 - x + 6 | Add | 3x^2 + 2x + 5 |
| Derivative | 5x^4 - 3x^2 + 8 | — | Differentiate | 20x^3 - 6x |
| Integral | 6x^2 - 4x + 9 | — | Integrate | 2x^3 - 2x^2 + 9x + C |
Formula Used
General polynomial: f(x) = anxn + an-1xn-1 + ... + a1x + a0
Evaluation: Substitute the chosen value of x into each term, then sum all term contributions.
Addition and subtraction: Combine coefficients that share the same exponent.
Multiplication: Multiply every term in Polynomial A by every term in Polynomial B, then combine matching exponents.
Derivative: d/dx (anxn) = n·anxn-1
Integral: ∫ anxn dx = anxn+1 / (n+1) + C
This page accepts expanded single-variable polynomials with nonnegative integer exponents. Examples include 7x^4 - 3x + 9, x^3 + x - 2, and 0.5x^2 - 1.25.
How to Use This Calculator
- Enter your first polynomial in expanded form inside Polynomial A.
- Enter Polynomial B only if you want to add, subtract, or multiply expressions.
- Select the desired operation from the dropdown list.
- Type an x value when you choose the evaluation option.
- Set graph start, end, and step values for the plotted range.
- Press Submit to show the result above the form.
- Use the CSV button for tabular export and the PDF button for a printable result snapshot.
Frequently Asked Questions
1) What expressions does this calculator support?
It supports expanded one-variable polynomials in x, such as 4x^3 - 2x + 6. Parentheses and negative exponents are intentionally excluded here for reliable polynomial-only processing.
2) Can I use decimals in coefficients?
Yes. Decimal coefficients such as 0.25x^4 - 1.5x + 3 are accepted. The result table and graph will use decimal output where needed.
3) What happens during simplification?
Simplification combines like terms, removes zero terms, orders powers from highest to lowest, and rewrites the polynomial in a cleaner standard form.
4) How is multiplication performed?
Each term in Polynomial A multiplies every term in Polynomial B. After expansion, matching exponents are merged into a final simplified polynomial.
5) Why does the integral include C?
Indefinite integration always adds an arbitrary constant because many different antiderivatives produce the same derivative. That constant is shown as + C.
6) What does the graph display?
The graph plots the current result polynomial across your selected range. During evaluation, it plots Polynomial A and marks the chosen x coordinate.
7) What is included in the CSV download?
The CSV export includes the visible result table. For standard operations, it exports exponents and coefficients. For evaluation, it also includes x^n and term contributions.
8) Why might my input fail validation?
Validation fails when a term is not polynomial-safe, such as missing numbers after symbols, unsupported parentheses, or malformed powers like x^^2.