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Synthetic Division Calculator

Divide any polynomial by a linear binomial (x − r) using synthetic division. Get the full tableau, step-by-step breakdown, quotient, remainder, and factor check.

Polynomial & Divisor

Enter coefficients from highest to lowest degree, then the root r (dividing by x − r)

Enter 0 for missing terms (e.g. x³ + 0x² − 2x + 5)

Enter r, not −r. For (x + 3), enter −3.

Example Polynomials

Click to load example problems

Synthetic Division Tableau

The complete division table

Root / Divisor
Carry-down values
Result row
Remainder

Step-by-Step Solution

Every step explained clearly

Result

Quotient polynomial and remainder

Division Result

Enter polynomial and click
Calculate

How It Works

Step 1 Write the root r and the coefficients in a row.
Step 2 Bring down the first coefficient.
Step 3 Multiply it by r, write below the next coefficient.
Step 4 Add the column. Repeat until done.
Step 5 Last number = remainder. Rest = quotient coefficients.

Remainder Theorem

If P(x) ÷ (x − r) gives remainder = 0, then (x − r) is a factor of P(x), and r is a root/zero of the polynomial.