Polynomial Division Calculator
Divide polynomials to find the quotient and remainder. Enter coefficients from highest to lowest degree.
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Enter the coefficients of the dividend and divisor polynomials, from highest degree to lowest, separated by commas. The calculator performs polynomial long division.
- Enter dividend coefficients. List from highest to lowest degree. Use 0 for missing terms. For x^3 - 3x + 2, enter "1, 0, -3, 2".
- Enter divisor coefficients. Same format. For x - 1, enter "1, -1".
- Read the result. The quotient and remainder are displayed in polynomial notation.
About Polynomial Division
Polynomial long division works like numerical long division. You divide the leading term of the dividend by the leading term of the divisor, multiply, subtract, and repeat. The result is a quotient polynomial plus a remainder. This is useful for factoring, simplifying rational expressions, and finding oblique asymptotes. If the remainder is zero, the divisor is a factor of the dividend.
Frequently Asked Questions
How does polynomial long division work?
Divide the leading term of the dividend by the leading term of the divisor. Multiply the result by the entire divisor, subtract from the dividend, and repeat with the new polynomial until the degree of the remainder is less than the divisor.
What if the remainder is zero?
If the remainder is zero, the divisor divides the dividend evenly, meaning the divisor is a factor of the dividend polynomial.
What is the difference between polynomial long division and synthetic division?
Synthetic division is a shortcut that only works when the divisor is linear (degree 1). Polynomial long division works for any degree divisor. Both give the same result when applicable.