Synthetic Division Calculator
Divide a polynomial by (x − a) with the full working shown.
Enter your values
ⓘ Live results
Results
- 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
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.
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.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.