Adding and Subtracting Polynomials

teen doing algebra on a white board

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The word polynomial simply describes math equations that involve addition, subtraction, multiplication, division, or exponentiation of these terms, but can be seen in a variety of iterations including polynomial functions, which yield a graph with a range of answers along the variable coordinates (in this case "x" and "y").​ Typically taught in pre-algebra classes, the topic of polynomials is critical to understanding higher math like algebra and calculus, so it's important that students gain a firm understanding of these multi-term equations involving variables and are able to simplify and regroup in order to more easily solve for the missing values.

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What Are Polynomials?


In mathematics and especially algebra, the term polynomial describes equations with more than two algebraic terms (such as "times three" or "plus two") and typically involve the sum of several terms with different powers of the same variables, though can sometimes contain multiple variables like in the equation to the left.

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Polynomial Addition and Subtraction

A graph of a polynomial function of degree 3.


Adding and subtracting polynomials requires students to understand how variables interact with one another, when they are the same and when they are different. For instance, in the equation presented above, values attached to x and y can only be added to values attached to the same symbols.

The second part of the equation above is the simplified form of the first, which is achieved by adding similar variables. When adding and subtracting polynomials, one can only add like variables, which exclude similar variables that have different exponential values attached to them.

In order to solve these equations, a polynomial formula may be applied and graphed like in this image to the left.

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Worksheets for Adding and Subtracting Polynomials

Challenge students to simplify these polynomial equations.


When teachers feel their students have a basic understanding of the concepts of polynomial addition and subtraction, there are a variety of tools they can use to help students further their skills in the early stages of understanding Algebra.

Some teachers may want to print Worksheet 1, Worksheet 2Worksheet 3Worksheet 4, and Worksheet 5 to test their students on their understanding of simple addition and subtraction of basic polynomials. The results will provide insight for teachers into which areas of Algebra the students need improvement on and which areas they excel in to better gauge how to proceed with the curriculum.

Other teachers may prefer to walk students through these problems in the classroom or take them home to work independently with the help of online resources like these. 

No matter which method a teacher uses, these worksheets are sure to challenge students' comprehension of one of the fundamental elements of most Algebra problems: polynomials.