Long Division Calculator

The Long Division Calculator performs polynomial long division and shows how a dividend is divided by a divisor to obtain a quotient and, when needed, a remainder. Use the tool to work through the calculation and review the result.

Definite
Indefinite

with respect to

Upper Limit:

Lower Limit:

The Long Division Calculator performs polynomial long division and shows how a dividend is divided by a divisor to obtain a quotient and, when needed, a remainder.

Polynomial long division

Arrange both polynomials in descending powers. Divide the leading term of the dividend by the leading term of the divisor, multiply the divisor by that term, subtract, and repeat until the remaining degree is lower than the divisor.

Worked example

Divide x² + 5x + 6 by x + 2. The first term is x, giving x(x + 2) = x² + 2x. Subtracting leaves 3x + 6. The next term is 3, and 3(x + 2) = 3x + 6. The remainder is 0, so the quotient is x + 3.

Why use long division?

The method is useful for simplifying rational expressions, checking polynomial factors, and preparing expressions for integration or further algebraic work.

Frequently Asked Questions FAQ

What is the goal of polynomial long division?

It separates a polynomial dividend into a quotient and a remainder after division by another polynomial.

What happens when the remainder is zero?

The divisor divides the polynomial exactly, and the quotient gives the complete result.

Can you show a short example?

Dividing x²+5x+6 by x+2 gives x+3 with remainder 0.

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