Synthetic Division Calculator
Divide a polynomial by a linear factor using synthetic division — with the remainder check and the factored form when it divides evenly.
Quotient
x^2 − x − 2
Breakdown
- Remainder
- 0
- Divides evenly?
- yes
- Full division result
- (x^2 − x − 2)(x − 2)
- Dividend evaluated at c
- 0
Last updated:
FAQ
How does synthetic division work?
Write the dividend's coefficients, drop the first one down, multiply by c, add to the next coefficient, and repeat. The bottom row gives the quotient's coefficients; the last value is the remainder — long division compressed to arithmetic.
What does the remainder tell me?
By the Remainder Theorem, dividing by x − c leaves a remainder equal to p(c), the polynomial evaluated at c. A zero remainder means (x − c) is a true factor — the Factor Theorem — and you've found a root.
Why must the divisor be linear?
Synthetic division only handles x − c because each step multiplies by the single number c. For higher-degree divisors you need long division or generalized synthetic division with several rows — the speed comes precisely from this restriction.
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