Polynomial Division Calculator
Algebraic solver for dividing polynomials. Handles parsing, long division logic, and formats the output as quotient plus remainder term.
About
Polynomial division is a fundamental operation in algebra and calculus, used for finding asymptotes, partial fraction decomposition, and solving higher-degree equations. Manual calculation is tedious and prone to arithmetic errors. This tool parses symbolic polynomial strings to extract coefficients automatically. It applies the division algorithm to separate the polynomial part from the rational remainder. This ensures accuracy for students verifying homework or engineers modeling control systems.
Formulas
The division algorithm states that for any polynomial dividend and non-zero divisor, there exist unique polynomials Q and R such that:
Reference Data
| Component | Math Symbol | Example |
|---|---|---|
| Dividend | P(x) | 2x3 − 4x + 1 |
| Divisor | D(x) | x + 1 |
| Quotient | Q(x) | 2x2 − 2x − 2 |
| Remainder | R(x) | 3 |
| Form | Standard | Q(x) + R(x)D(x) |