ForHosting KIT · Developer Utilities

Polynomial division calculator

Polynomial division is the Euclidean algorithm on univariate polynomials: given a dividend p(x) and a non-zero divisor d(x), there exist unique polynomials q(x) and r(x) such that p equals d times q plus r, and either r is the zero polynomial or the degree of r is strictly less than the degree of d.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Students meet this identity when they first divide x-squared minus three x plus two by x minus one and recover the linear quotient x minus two. Engineers meet it when they cancel a factor, reduce a transfer function, or compute a remainder for later evaluation. This polynomial division calculator accepts both polynomials as dense coefficient arrays in descending degree order, rejects the zero polynomial as a divisor, and returns the quotient and remainder arrays together with degrees and compact polynomial strings. The same pure function powers the free browser widget and the prepaid API, so homework checks, computer-algebra smoke tests, and edge workers never disagree on a coefficient.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/math/polynomial-division

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/math/polynomial-division \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"dividend":[1,-3,2],"divisor":[1,-1]}'

const res = await fetch("https://api.kit.forhosting.com/math/polynomial-division", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "dividend": [
      1,
      -3,
      2
    ],
    "divisor": [
      1,
      -1
    ]
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/math/polynomial-division",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "dividend": [
        1,
        -3,
        2
    ],
    "divisor": [
        1,
        -1
    ]
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/polynomial-division", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"dividend":[1,-3,2],"divisor":[1,-1]}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"dividend":[1,-3,2],"divisor":[1,-1]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/polynomial-division", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "dividend": [
    1,
    -3,
    2
  ],
  "divisor": [
    1,
    -1
  ]
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "math.polynomial_division",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Limits

`max_degree`	64
`max_abs_coeff`	1000000000000000

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →