Synthetic Division Calculator
How It Works
This synthetic division calculator uses established formulas to provide accurate results.
The basic rule:
- Bring down leading coefficient
- Multiply by c, add to next coefficient
- Repeat until done
- Last number is the remainder
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is synthetic division?
Synthetic division is a shortcut for dividing a polynomial by a linear factor (x - c). It uses only the coefficients and is much faster than long division. It only works when dividing by (x - c), not more complex divisors.
What is the Factor Theorem?
The Factor Theorem states that (x - c) is a factor of polynomial P(x) if and only if P(c) = 0. So if synthetic division gives a remainder of 0, then (x - c) is a factor.
What is the Remainder Theorem?
The Remainder Theorem says that the remainder when P(x) is divided by (x - c) is equal to P(c). Synthetic division efficiently calculates this.
Can synthetic division handle higher degree polynomials?
Yes, synthetic division works for any degree polynomial divided by (x - c). The process is the same: bring down, multiply, add, repeat.