How to Add Polynomial Equations

Learning to add polynomial equations can be daunting when you first begin, particularly if you have little experience with polynomial terms. Nonetheless, once you dive into it, adding polynomial expressions together is a breeze. All you have to do is identify and add like terms!

Difficulty: Moderately Easy

Instructions

Instructions

1. Learn what a polynomial equation is. You may not know it yet, but you have probably already come across algebra equations which are polynomials. Anything constructed of multiple terms and constants is a polynomial. A constant is just a normal number such as 5. A term is any letter variable such as X, or Y^2. (5x^2 + 8x - 2) + (4 + 2x^2 - 3x) is a pretty typical polynomial equation with two terms and a constant.

2. Write the problem out neatly on a piece of paper with a pencil. Even if the problem is written in your math book, it is always a good idea to copy it yourself. It forces you to look closely at the math equation and makes it easier to check your work. In addition, many teachers require it.

3. Arrange both polynomials in order of degree if they aren't already arranged that way. Degree is a measure of the exponent attached to each term. Using an example from step one, 5x^2 is a second degree term, while 4 is considered to have a degree of zero.

4. Set up an addition problem. Arrange one polynomial on top of the other, removing the parentheses and lining up like terms. For example, (5x^2 +8x - 2) + (2x^2 - 3x + 4) becomes:
   5x^2 + 8x - 2
   + 2x^2 - 3x + 4

5. Solve the problem by combining like terms. To continue with the example above:
   
   5x^2 + 8x - 2
   + 2x^2 - 3x + 4
   ------------------
   7x^2 + 5x + 2

Tips & Warnings

• Always use a pencil when doing math. Erasing is easier and neater than crossing out mistakes.
• Once you get good at adding polynomials, you can skip step 4 and go straight to combining like terms.
• Be sure not to forget subtraction signs. This is one of the most common sources of error. In the problem above, for example, it would be easy to drop the minus from 3x, resulting in an incorrect answer.

Resources

• Good demonstration of how to add polynomials.