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:
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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