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Polynomial Division Calculator

Divide any polynomial by another using long division or synthetic division — with full step-by-step work, remainder theorem, and factor check.

Enter coefficients or expressions like x^3 - 2x + 5  ·  Supports any degree polynomial

Polynomials

Enter dividend and divisor as expressions or coefficient lists

Syntax: Use x^3, x^2, x for terms. Coefficients like 2x^2, -5x, 7. Spaces, + and − signs are fine. Missing terms (e.g. x^3 + 1) are handled automatically.

Method

Synthetic division requires a linear divisor (x − c)

Examples

Classic polynomial division problems

Division Result

Quotient Q(x)
—
Remainder R(x)
—
Dividend degree—
Divisor degree—
Quotient degree—
Is factor?—
Method used—

Division Algorithm

P(x) = D(x) · Q(x) + R(x) where deg(R) < deg(D)

Tips

• If R = 0, D(x) is a factor of P(x)

• Remainder Theorem: R = P(c) when dividing by (x − c)

• Synthetic division only works for (x − c)

• Always arrange by descending degree