Polynomial Addition Calculator

About this calculator

Adding two polynomials means combining like terms — the coefficients of matching powers of x are added together, while terms of a degree that appears in only one polynomial simply carry over unchanged. Working with polynomials as ordered lists of coefficients, aligned by degree from highest to lowest (or lowest to highest, depending on convention), makes this addition mechanical: pad the shorter list with zeros where needed and add position by position.

This operation underlies algebra coursework on polynomial arithmetic, but it also shows up wherever quantities are modeled as polynomials in applied math and engineering — combining transfer functions in control systems, adding series expansions in physics, or working with polynomial representations inside a computer algebra system, all reduce to the same coefficient-by-coefficient addition.

Enter the coefficients of two polynomials and the calculator aligns them by degree and returns the coefficients of their sum.