Polynomial Long Division Calculator
Polynomial Long Division Calculator
Enter the coefficients of the dividend and divisor polynomials (highest degree first, separated by commas), and this calculator performs the long division.
Polynomial long division follows essentially the same repeated process as numerical long division — divide the leading terms, multiply the result back through the divisor, and subtract — continuing until whatever remains has a lower degree than the divisor, at which point that remainder can't be divided further. Coefficients are entered from the highest degree down to the constant term, so x² − 3x + 2 becomes "1, -3, 2" — this operation is a core building block in algebra for simplifying rational expressions, finding polynomial roots, and factoring higher-degree polynomials that don't factor neatly by inspection.
- Polynomial long division works much like numerical long division, repeatedly dividing the leading terms, multiplying back, and subtracting until the remainder's degree is smaller than the divisor's.
- Enter coefficients from the highest degree down to the constant term, e.g. x² − 3x + 2 is entered as "1, -3, 2".
- A remainder of 0 means the divisor divides the dividend evenly, which also means the divisor is a factor of the dividend.
How do I perform polynomial long division?
Divide the leading term of the dividend by the leading term of the divisor to get the next quotient term, multiply the entire divisor by that term and subtract it from the dividend, then repeat with the new remainder until its degree is lower than the divisor's.
What is (x² − 3x + 2) ÷ (x − 1)?
x − 2, with a remainder of 0, since (x − 1)(x − 2) = x² − 3x + 2.
Polynomial Long Division Calculator
Enter the coefficients of the dividend and divisor polynomials (highest degree first, separated by commas), and this calculator performs the long division.
Polynomial long division follows essentially the same repeated process as numerical long division — divide the leading terms, multiply the result back through the divisor, and subtract — continuing until whatever remains has a lower degree than the divisor, at which point that remainder can't be divided further. Coefficients are entered from the highest degree down to the constant term, so x² − 3x + 2 becomes "1, -3, 2" — this operation is a core building block in algebra for simplifying rational expressions, finding polynomial roots, and factoring higher-degree polynomials that don't factor neatly by inspection.
- Polynomial long division works much like numerical long division, repeatedly dividing the leading terms, multiplying back, and subtracting until the remainder's degree is smaller than the divisor's.
- Enter coefficients from the highest degree down to the constant term, e.g. x² − 3x + 2 is entered as "1, -3, 2".
- A remainder of 0 means the divisor divides the dividend evenly, which also means the divisor is a factor of the dividend.
How do I perform polynomial long division?
Divide the leading term of the dividend by the leading term of the divisor to get the next quotient term, multiply the entire divisor by that term and subtract it from the dividend, then repeat with the new remainder until its degree is lower than the divisor's.
What is (x² − 3x + 2) ÷ (x − 1)?
x − 2, with a remainder of 0, since (x − 1)(x − 2) = x² − 3x + 2.