Polynomial Long Division Calculator

Quick start

1. In the first box, type the dividend's coefficients from the highest power down. For x³ − 6x² + 11x − 6, type 1, -6, 11, -6.
2. In the second box, type the divisor's coefficients. For x − 1, type 1, -1.
3. Use 0 for any missing power, so x² + 4 is 1, 0, 4.

The four-step cycle

Polynomial long division repeats the same cycle until the leftover has a lower degree than the divisor:

1. Divide the leading term of what is left by the leading term of the divisor.
2. Write that result in the quotient.
3. Multiply the whole divisor by it.
4. Subtract, and bring down the next term.

Example: (x³ − 6x² + 11x − 6) ÷ (x − 1)

x³ ÷ x = x². Subtract x²(x − 1) to leave −5x² + 11x. Next, −5x² ÷ x = −5x; subtract to leave 6x − 6. Finally 6x ÷ x = 6, and subtracting leaves 0. The quotient is x² − 5x + 6 and the remainder is 0, so x − 1 is a factor.

Writing the answer

Every division can be written as dividend = divisor × quotient + remainder. When the remainder is not zero, the result is often written as quotient + remainder ÷ divisor.

Common questions