Synthetic Division Calculator
Enter a polynomial's coefficients below to instantly divide by (x − c), with every step shown.
How Synthetic Division Works
Bring down the first coefficient, multiply it by c, add that to the next coefficient, and repeat. The last number produced is the remainder; everything before it is the quotient's coefficients.
Worked example
Divide x³ − 6x² + 11x − 6 by (x − 1).
1, then −6 + 1(1) = −5, then 11 + (−5)(1) = 6, then −6 + 6(1) = 0
Quotient: x² − 5x + 6, remainder 0
Frequently Asked Questions
What is synthetic division?
Synthetic division is a shortcut for dividing a polynomial by a linear factor (x − c), using only the coefficients instead of writing out the full long-division process.
When can you use synthetic division?
Only when dividing by a linear expression of the form x − c. For any other divisor, you need regular polynomial long division instead.
What does a remainder of 0 tell you?
A remainder of 0 means (x − c) divides evenly into the polynomial, which means c is a root of the polynomial and (x − c) is one of its factors.
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