How does the Synthetic Division work?

Write coefficients in a row Then: Drop first coefficient; multiply by root r Then: Add to next coefficient; repeat Then: Last value is remainder; others are quotient coefficients.

Can you give an example of how to use the Synthetic Division?

Example: Input x³−6x²+11x−6 ÷ (x−1) gives a result of Quotient: x²−5x+6, Remainder: 0 (so x=1 is a root).

Is the Synthetic Division free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Synthetic Division?

Our Synthetic Division uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Synthetic Division

Synthetic Division Calculator

Polynomial Coefficients (highest degree first)

Divisor Root (x = ?)

Synthetic division is a shorthand method for dividing a polynomial by a linear factor (x − r). It is faster than long division and directly tests whether r is a root of the polynomial.

Symbol	Name	Unit	Description
P(x)	polynomial to divide	—	—
(x − c)	linear divisor	—	—
c	value	—	—

Step	Action
1	Write root r and coefficients
2	Drop leading coefficient
3	Multiply by r, add to next coefficient
4	Repeat until remainder
5	Remainder = 0 means r is a root

References

›Synthetic division — Khan Academy

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Synthetic Division

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