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Polynomial Long Division Calculator

Enter coefficients from highest degree to constant term

Dividend coefficients
Divisor coefficients

Long Division Identity

Dividend = Divisor × Quotient + Remainder

Polynomial long division follows the same idea as numerical long division. At each step, divide the leading term of the current dividend by the leading term of the divisor, multiply back, subtract, and repeat until the remaining polynomial has lower degree than the divisor. The final result is a quotient polynomial plus a remainder polynomial, and the answer can always be checked by multiplying the divisor by the quotient and adding the remainder.

Note: Enter coefficients in descending degree order. For x³-3x²+2x+4, enter 1,-3,2,4.

What Is Polynomial Long Division?

Polynomial long division is the polynomial version of arithmetic long division. It divides a dividend polynomial by a divisor polynomial and produces a quotient plus a remainder.

Quotient

The polynomial result of the division.

Remainder

The leftover polynomial with degree lower than the divisor.

Leading Term

Each step divides leading terms to decide the next quotient term.

Verification

The final answer should satisfy dividend = divisor × quotient + remainder.

💡 Example: Divide x³-3x²+2x+4 by x-1. The quotient is x²-2x and the remainder is 4.

Applications of Polynomial Long Division

Polynomial DivisionRational ExpressionsFactorization

Frequently Asked Questions

What is a polynomial long division calculator?
A polynomial long division calculator divides one polynomial by another and returns the quotient, remainder, and steps.
What order should coefficients use?
Enter coefficients in descending degree order, from the leading term to the constant term.
What does the remainder mean?
The remainder is the part left after division and must have degree lower than the divisor.
Can the divisor be a constant?
Yes, but polynomial long division is most useful when dividing by a non-constant polynomial.
How do I check the answer?
Verify Dividend = Divisor × Quotient + Remainder.

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