Enter coefficients from highest degree to constant term
Dividend coefficients
Divisor coefficients
Result
Quotient
Remainder
Step-by-Step Derivation
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.
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