{
  "title": "Polynomial division walkthrough",
  "human_url": "https://happytails.ai/en/calculators/polynomial-division-walkthrough/",
  "agent_url": "https://happytails.ai/agents/en/calculators/polynomial-division-walkthrough/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/polynomial-division-walkthrough.md",
  "content": "Polynomial division walkthrough\nDivide one polynomial by another with exact fractions and see every long or synthetic division step. The result shows the quotient, the remainder and a checked identity.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Polynomial division walkthrough\nType the dividend polynomial, such as 2x^4 - 3x^3 + 5x - 7.\nEnter the divisor and choose long or synthetic division.\nRun the division and read each step, the quotient and the remainder.\nDownload the JSON report or the CSV table of steps.\nUseful next steps\nQuadratic formula calculator\nFractions\nGraphing calculator\nHow the division works\nEach step divides the leading term of the current remainder by the leading term of the divisor, multiplies the divisor by that quotient term and subtracts. Synthetic division does the same work for a divisor x - c using only coefficients. All arithmetic uses exact fractions, so 1/3 stays 1/3. The tool then checks that divisor times quotient plus remainder equals the dividend exactly. Method: OpenStax, College Algebra 2e, section 5.4 Dividing Polynomials (2021).\nWhat you can enter\nUse one variable, whole-number powers and numbers such as 3, 0.25 or 1/2. You can write 2x for 2*x and 3(x+1) for 3*(x+1). Functions, other variables and negative powers are rejected with a message instead of being guessed.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Quadratic formula calculator",
      "url": "https://happytails.ai/en/calculators/quadratic-formula/"
    },
    {
      "name": "Fractions",
      "url": "https://happytails.ai/en/calculators/fractions/"
    },
    {
      "name": "Graphing calculator",
      "url": "https://happytails.ai/en/calculators/graphing-calculator/"
    }
  ],
  "tool": {
    "id": "polynomial-division-walkthrough",
    "category": "calculators",
    "built": true,
    "requirements": "Each polynomial is limited to 1,000 characters, 512 symbols, 24 nesting levels, degree 64 and 100 digits per number; exact values may grow to 1,024 digits. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV table of steps.",
    "implementation": {
      "fields": [
        {
          "key": "divisor",
          "label": "Divisor",
          "value": "x - 3",
          "type": "text",
          "maxLength": 1000,
          "help": "Enter a nonzero polynomial in the same variable, such as x - 3 or 2x^2 + 1. Fractions such as 1/2 are allowed."
        },
        {
          "key": "method",
          "label": "Method",
          "value": "Long division",
          "type": "select",
          "values": [
            "Long division",
            "Synthetic division"
          ]
        }
      ],
      "registrationFamily": "exact-math-reference",
      "inputMaxLength": 1000,
      "inputErrorCode": "EXACT_MATH_REFERENCE_EXPRESSION_TOO_LONG",
      "note": "Divides exactly on your device with fractions, up to degree 64 and 1,000 characters per polynomial. Synthetic division needs a divisor of the form x - c.",
      "experience": {
        "automatic": false,
        "single": true,
        "inputMaxLength": 1000,
        "inputMode": "text",
        "label": "Dividend polynomial",
        "placeholder": "2x^4 - 3x^3 + 5x - 7",
        "help": "One variable, whole-number powers and exact numbers such as 1/2. Up to 1,000 characters. Review the settings before running.",
        "action": null
      },
      "mode": "explicit",
      "interactive": false
    },
    "execution": "Browser interface",
    "api": null,
    "browser_agent": {
      "supported": true,
      "name": "run_current_tool",
      "discovery": "WebMCP on the human page in a supporting browser",
      "verification": "See audit/API-AUDIT.md; availability is not verification"
    }
  },
  "markdown": "# Polynomial division walkthrough\n\n- Human page: https://happytails.ai/en/calculators/polynomial-division-walkthrough/\n- Markdown: https://happytails.ai/en/calculators/polynomial-division-walkthrough.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/polynomial-division-walkthrough/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `polynomial-division-walkthrough` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Use the visible action or interactive controls. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nDivides exactly on your device with fractions, up to degree 64 and 1,000 characters per polynomial. Synthetic division needs a divisor of the form x - c.\n\n### Inputs and settings\n\nText input: Dividend polynomial.\n\nExample or placeholder shown in the interface (not a validated fixture):\n\n```text\n2x^4 - 3x^3 + 5x - 7\n```\n\nOne variable, whole-number powers and exact numbers such as 1/2. Up to 1,000 characters. Review the settings before running.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `divisor` | Divisor | text | \"x - 3\" |  |\n| `method` | Method | select | \"Long division\" | Allowed: Long division, Synthetic division |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nEach polynomial is limited to 1,000 characters, 512 symbols, 24 nesting levels, degree 64 and 100 digits per number; exact values may grow to 1,024 digits. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV table of steps.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"polynomial-division-walkthrough\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Each polynomial is limited to 1,000 characters, 512 symbols, 24 nesting levels, degree 64 and 100 digits per number; exact values may grow to 1,024 digits. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV table of steps.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"divisor\",\n        \"label\": \"Divisor\",\n        \"value\": \"x - 3\",\n        \"type\": \"text\",\n        \"maxLength\": 1000,\n        \"help\": \"Enter a nonzero polynomial in the same variable, such as x - 3 or 2x^2 + 1. Fractions such as 1/2 are allowed.\"\n      },\n      {\n        \"key\": \"method\",\n        \"label\": \"Method\",\n        \"value\": \"Long division\",\n        \"type\": \"select\",\n        \"values\": [\n          \"Long division\",\n          \"Synthetic division\"\n        ]\n      }\n    ],\n    \"registrationFamily\": \"exact-math-reference\",\n    \"inputMaxLength\": 1000,\n    \"inputErrorCode\": \"EXACT_MATH_REFERENCE_EXPRESSION_TOO_LONG\",\n    \"note\": \"Divides exactly on your device with fractions, up to degree 64 and 1,000 characters per polynomial. Synthetic division needs a divisor of the form x - c.\",\n    \"experience\": {\n      \"automatic\": false,\n      \"single\": true,\n      \"inputMaxLength\": 1000,\n      \"inputMode\": \"text\",\n      \"label\": \"Dividend polynomial\",\n      \"placeholder\": \"2x^4 - 3x^3 + 5x - 7\",\n      \"help\": \"One variable, whole-number powers and exact numbers such as 1/2. Up to 1,000 characters. Review the settings before running.\",\n      \"action\": null\n    },\n    \"mode\": \"explicit\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nDivide one polynomial by another with exact fractions and see every long or synthetic division step. The result shows the quotient, the remainder and a checked identity.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Polynomial division walkthrough\n\n1. Type the dividend polynomial, such as 2x^4 - 3x^3 + 5x - 7.\n2. Enter the divisor and choose long or synthetic division.\n3. Run the division and read each step, the quotient and the remainder.\n4. Download the JSON report or the CSV table of steps.\n\n## Useful next steps\n\n- [Quadratic formula calculator](https://happytails.ai/en/calculators/quadratic-formula/) ([Markdown](https://happytails.ai/en/calculators/quadratic-formula.md))\n\n- [Fractions](https://happytails.ai/en/calculators/fractions/) ([Markdown](https://happytails.ai/en/calculators/fractions.md))\n\n- [Graphing calculator](https://happytails.ai/en/calculators/graphing-calculator/) ([Markdown](https://happytails.ai/en/calculators/graphing-calculator.md))\n\n## How the division works\n\nEach step divides the leading term of the current remainder by the leading term of the divisor, multiplies the divisor by that quotient term and subtracts. Synthetic division does the same work for a divisor x - c using only coefficients. All arithmetic uses exact fractions, so 1/3 stays 1/3. The tool then checks that divisor times quotient plus remainder equals the dividend exactly. Method: OpenStax, College Algebra 2e, section 5.4 Dividing Polynomials (2021).\n\n### What you can enter\n\nUse one variable, whole-number powers and numbers such as 3, 0.25 or 1/2. You can write 2x for 2\\*x and 3(x+1) for 3\\*(x+1). Functions, other variables and negative powers are rejected with a message instead of being guessed.\n"
}