Adding Polynomials

Step By Step Procedure for Easy Learning

Adding polynomials is easy, especially with the step by step procedure outlined here.

So if you have had any problem in adding two polynomials or are into it for the very first time then I am sure you are going to find this article very useful.

Before getting onto the details of the process let me give you a taste of the two basic styles of polynomial addition.

Horizontal Addition of Polynomials

This method is very similar to the addition of real number following the horizontal method. However it has its own rules of addition. So if you want to have some polynomial addition help then read on for more about this method.

Vertical Addition of Polynomials

Vertical method of addition of polynomials is based around the same principle as the horizontal method but then the arrangement of terms is vertical unlike the other method.

If you ask me, there are no specific advantages or disadvantages of either of the methods. It’s a matter of personal preference and choice. Follow the method that you are comfortable with.

Adding Polynomials Horizontally

To explain this method let me take an example of adding two polynomials.

The polynomials to be added are

• 2x + 3y
• 6x + 7y

Step #1 Arrange the polynomials to be added in a horizontal line

(2x + 3y) + (6x + 7y)

= 2x + 3y + 6x + 7y

Step #2 Reorganize the terms by placing the ones with similar variables

= 2x + 3y + 6x + 7y

= 2x + 6x + 3y + 7y

Step #3 Add the coefficients of terms with similar variable.

= 2x + 6x + 3y + 7y

= (2 + 6)x + (3 + 7)y

= 8x + 10y

That’s the answer to the adding polynomials question we took up.

Adding Polynomials Vertically

Let us take the same example as above and illustrate the vertical addition process.

So the polynomials to be added are 2x + 3y and 6x + 7y.

Step #1 Arrange the two polynomials vertically such that the similar variable terms are placed in a single vertical line.

2x + 3y

+ 6x + 7y

Step #2 Add the coefficients of the similar variable terms placed in a vertical line.

2x + 3y

+ 6x + 7y

Adding the vertical coefficients we get

8x + 10y

Here the coefficients of y are 3 and 7. Upon adding the two we get 10. Thus the resultant coefficient of variable y becomes 10.

Step #3 The result thus found is the sum of the two polynomials we had started with.