Polynomial Division
Divide polynomials by long division or synthetic division and apply the remainder theorem, with every subtraction shown. Try “divide x³ + 2x² − 5x + 1 by x − 2”.
Try an example:
What you can do with the Polynomial Division
Long division and synthetic division, remainder theorem.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. divide x^3 + 2x^2 - 5x + 1 by x - 2
How the Polynomial Division works
- Write both polynomials in descending powers, adding 0 coefficients for missing terms.
- Divide the leading terms, multiply back, subtract, and bring down the next term.
- Repeat until the remainder has lower degree than the divisor.
Frequently asked questions
What is the remainder theorem?
The remainder when f(x) is divided by (x − a) equals f(a).
When can I use synthetic division?
When the divisor is linear and of the form x − a. It is a faster, shorter version of long division.
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