Synthetic Division Calculator
Divide a polynomial by (x − a) with the full working shown.
Enter your values
Enter the coefficients, highest power first you are working with.
Enter the divide by (x − a), a = you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Quotient
- 2x^2 + 0x + 2
- Remainder
- 5
- Exact division?
- No
- Quotient degree
- 2
Working
- 1Bring down 2
- 2-6 + 3 × 2 = 0
- 32 + 3 × 0 = 2
- 4-1 + 3 × 2 = 5
Quick answer
Synthetic division is a shorthand for dividing by (x − a): bring down the leading coefficient, multiply by a, add to the next coefficient and repeat.
bᵢ = aᵢ + a·bᵢ₋₁
At a glance
| What it does | Divide a polynomial by (x − a) with the full working shown. |
|---|---|
| Category | Math |
| Inputs needed | Coefficients, highest power first, Divide by (x − a), a = |
| Main output | Quotient |
| Formula | bᵢ = aᵢ + a·bᵢ₋₁ |
| Cost | Free — no sign-up, no download |
How to use the Synthetic Division Calculator
- 1Type every coefficient from the highest power down, including zeros.
- 2Enter a from the divisor (x − a) — for (x + 2), a is −2.
- 3Read the quotient coefficients and the remainder, with each step shown.
Inputs explained
- Coefficients, highest power first
- Enter the coefficients, highest power first you are working with.
- Divide by (x − a), a =
- Enter the divide by (x − a), a = you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Coefficients, highest power first2, -6, 2, -1
- Divide by (x − a), a =3
Results
- Quotient2x^2 + 0x + 2
- Remainder5
- Exact division?No
- Quotient degree2
- Bring down 2
- -6 + 3 × 2 = 0
- 2 + 3 × 0 = 2
- -1 + 3 × 2 = 5
Frequently asked questions
Can I divide by 2x − 3?
Yes: use a = 1.5, then divide the whole quotient by 2 afterwards.
Why include zero coefficients?
Synthetic division is positional — a missing x² term must appear as 0 or the columns shift.
What do I need to enter into the Synthetic Division Calculator?
Just 2 values: coefficients, highest power first, divide by (x − a), a =. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Synthetic Division Calculator work out the answer?
Synthetic division is a shorthand for dividing by (x − a): bring down the leading coefficient, multiply by a, add to the next coefficient and repeat. It applies the formula bᵢ = aᵢ + a·bᵢ₋₁ and shows the working so you can check each step by hand.
Is the Synthetic Division Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.