Q:

What are polynomial operations?

A:

Polynomial operations are basic math operations performed with polynomials instead of integers. A polynomial is an algebraic expression with more than one term. While there are algebraic polynomial operations, simple operations such as addition, multiplication, subtraction and division are also examples of polynomial operations.

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Adding polynomials is a matter of combining like terms. If a polynomial includes the terms 3x and 4x they are like terms and add together to form 7x. Similarly, 2xy and 3xy add to form 5xy. However, it is not possible to combine the terms 4x and 2xy as they are not like terms. To subtract one polynomial from a second the signs of each term of the subtracted polynomial are changed and the two polynomials are added.

To multiply polynomials, multiply every term in the first polynomial by every term in the second polynomial. Once the multiplication process is completed, it is necessary to combine terms to form a final answer. Multiplication with large polynomials becomes highly tedious.

Mathematicians also divide one polynomial by another. In the simplest of division problems, it is possible to factor the polynomials and eliminate one or more factors. In more complex division problems, the mathematician uses polynomial long division or synthetic division to find the answer.

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