Synthetic Division Calculator
Divide polynomials fast using synthetic division with step-by-step solutions
Perform Synthetic Division
How to use:
Enter polynomial coefficients in descending order. For x³ - 2x + 1, enter: 1, 0, -2, 1
Enter in order: coefficient of highest power first
For (x - 2), enter 2. For (x + 3), enter -3
Result:
Steps:
Frequently Asked Questions
What is synthetic division?
Synthetic division is a shortcut method for dividing polynomials by linear factors of the form (x - c). It's faster than long division and uses only the coefficients, making calculations simpler and more efficient.
When can you use synthetic division?
You can only use synthetic division when dividing by a linear polynomial (degree 1) in the form (x - c). For divisors like (x² + 1) or (2x - 3), you must use long division instead.
How do you interpret the remainder?
If the remainder is 0, then (x - c) is a factor of the polynomial. A non-zero remainder means (x - c) is not a factor. The remainder also represents f(c) by the Remainder Theorem.
What if there's a missing term?
Use 0 as the coefficient for any missing terms. For x³ + 5 (no x² or x terms), write coefficients as: 1, 0, 0, 5. This ensures proper alignment during synthetic division.
How do you handle (x + c)?
Rewrite (x + c) as (x - (-c)) and use -c as your divisor. For example, dividing by (x + 3) means using -3 in synthetic division, not +3.
What is the Remainder Theorem?
The Remainder Theorem states that when polynomial f(x) is divided by (x - c), the remainder equals f(c). This provides a quick way to evaluate polynomials and is closely related to the Factor Theorem.