Polynomial Multiplication Calculator

The polynomial multiplication calculator takes two univariate polynomials, each represented as a set of coefficients, and multiplies them together to generate the resulting polynomial.

This page exists due to the efforts of the following people:




Created: 2018-02-27 18:36:09, Last updated: 2023-04-02 15:20:45
Creative Commons Attribution/Share-Alike License 3.0 (Unported)

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/7743/. Also, please do not modify any references to the original work (if any) contained in this content.

The user enters the coefficients for each polynomial separated by space, where a coefficient can be any number type (integer, real, or complex). If a polynomial term is empty, the coefficient for that term should be zero.

The calculator first checks the degree of each polynomial, which is determined by the highest power of the variable in the polynomial. It then multiplies the coefficients of each term in one polynomial by each term in the other polynomial and combines the like terms, simplifying the resulting polynomial as much as possible.

PLANETCALC, Polynomial multiplication

Polynomial multiplication


Polynomial multiplication formula:
(arxr + ... + a0)(bsxs + ... + b0)=pr+sxr+s + ... + p0,
where pk=a0bk + a1bk-1 + ... + ak-1b1 + akb0
Note: ai = 0 when i>r and bj = 0 when j>s 1

  1. Donald E. Knuth The art of computer programming. Third edition. Vol. 2. Seminumerical Algorithms 

URL copied to clipboard
PLANETCALC, Polynomial Multiplication Calculator