Math · Algebra

Synthetic Division Calculator

Divide any polynomial by (x − c) using the fast synthetic method — quotient, remainder and the full algorithm rows.

Polynomial (e.g. 2x^3 - 5x^2 + 4x - 1)

c in divisor (x − c)

Result

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Setup: write the coefficients of the polynomial (all degrees present), then carry down the leading coefficient.
Repeat: multiply by c, add to the next column. The last number is the remainder r; by the Remainder Theorem f(c) = r. If r = 0, (x − c) is a factor.

Factor theorem

Zero remainder means x − c is a factor and c is a root.

Full algorithm rows

Top coefficients, middle products and bottom quotient all shown.

Remainder check

f(c) verified by direct evaluation.

Instant results

Every keystroke rebuilds the synthetic division table.

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