Polynomial Long Division Calculator - Step-by-Step Solutions

Enter the dividend and the divisor. The calculator divides the polynomials by long division and shows the quotient, the remainder and every step of the division. When the divisor is of the first degree, such as $x - 3$ or $2x + 1$, it also divides with Horner's scheme (synthetic division).

Examples: $(2x^3 + 3x^2 - 5x + 6) \div (x + 3)$ $(x^3 - 8) \div (x - 2)$ $(x^4 + 3x^2 + 2x - 8) \div (x^2 - 3x)$ $(3x^3 - 5x^2 + 2x + 3) \div (2x - 1)$ $(x^3 + y^3) \div (x + y)$ $(6x^3y - 4x^2y^2 + 5x) \div (2xy)$

How to enter the polynomials

• Write powers with ^: x^2 is $x^2$ and (x+1)^3 is $(x+1)^3$.
• The multiplication sign can be left out: 3xy, 2(x+1), (x+1)(x-2). You can also write 3*x*y.
• Every letter is a variable of its own, so xy means ${x \cdot y}$.
• Coefficients can be fractions or decimals: x^2/4 - 1, 0.5x^2 - 2.
• Brackets are multiplied out first, so the dividend can also be a product: (x+1)(x^2+3).
• You can also type the whole division in the box of the dividend, as (x^3 - 8)/(x - 2), and leave the divisor empty.

How the calculator divides

• The answer is written as dividend = divisor · quotient + remainder, where the remainder is of a lower degree than the divisor.
• A divisor of one term, such as $2xy$, divides every term of the dividend. The terms it does not divide make up the remainder.
• A longer divisor is divided by long division: divide the leading term of the dividend by the leading term of the divisor, multiply the divisor by the result, subtract, and repeat with what is left.
• With more than one variable, the division goes by the powers of one letter, whose highest power in the divisor has a number as its coefficient. A divisor such as $xy + 1$ cannot be divided this way.
• For a divisor of the form $x - a$ or $mx + n$, the calculator also shows Horner's scheme. Its last number is the remainder, which is also the value of the dividend at the root of the divisor.

Other resources involving polynomial division

Polynomial long division Horner's method Factoring Polynomials Calculator Simplifying polynomial expressions - problems with solutions