Polynomial Long Division

Divide polynomials with quotient and remainder

x^3 − 2x^2 + 5 = (x − 3)(x^2 + x + 3) + (14)

Quotient Q(x)

x^2 + x + 3

Remainder R(x)

Check: P(x) = D(x) · Q(x) + R(x)

x^3 − 2x^2 + 5 = (x − 3)(x^2 + x + 3) + (14)

About this calculator

The Polynomial Long Division calculator divides one polynomial by another and returns the quotient and remainder, with a worked long-division tableau that shows each elimination step. Enter coefficients highest power first. Useful for algebra, factoring, partial fractions, and finding asymptotes.

Common examples

(x³ − 2x² + 5) ÷ (x − 3) → quotient x² + x + 3, remainder 14
(x² − 5x + 6) ÷ (x − 2) → quotient x − 3, remainder 0
(2x² + 3x − 2) ÷ (2x − 1) → quotient x + 2, remainder 0
(x² + 1) ÷ (2x) → quotient 0.5x, remainder 1