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Synthetic Division Calculator

The three-row tableau for (x − a), including fractional a such as 1/2 and non-monic divisors, with the remainder theorem and the factor theorem spelled out.

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Synthetic Division Calculator is free to use as often as you like, directly from this page. You will find it under Algebra & equations, with Polynomial Long Division Calculator and Long Division Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Synthetic Division Calculator?

The three-row tableau for (x − a), including fractional a such as 1/2 and non-monic divisors, with the remainder theorem and the factor theorem spelled out.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Synthetic Division Calculator different from Polynomial Long Division Calculator?

They sit next to each other but answer different questions: Polynomial Long Division Calculator is the one to open when you need it to the whole tableau, subtraction row by subtraction row, with quotient, remainder and the identity dividend = divisor × quotient + remainder checked for you. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Long Division Calculator is the closest one after this: Divide two whole numbers to get the quotient, remainder and exact decimal result.

What else is worth having open alongside it?

Absolute Value Equation Solver and Absolute Value Inequality Solver — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.ExplainerOrder of Operations (PEMDAS / BODMAS): Why the Order MattersPEMDAS and BODMAS are two names for one rule that fixes the order you evaluate a math expression — so everyone gets the same answer. Learn the rule with a worked example.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.