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Adding Polynomials


One of the most important things you can do to be successful in this lesson is to be observant.  When adding (and in the following lesson subtracting) polynomials, you will categorize each term in the polynomial by its degree.  You may only like terms of the same degree.


Note:  Many courses teach adding polynomial and subtracting polynomials at the same time.  However, this topic has been broken into two separate lessons that contain a more step-by-step approach.  It is highly recommended that work though these two lessons in order, starting with this one and then moving onto subtracting polynomials.



A polynomial is simply an expression containing algebraic terms.  In this lesson, you will be adding and subtracting polynomials.  Being observant concerning every coefficient and exponent will help you quickly and accurately find the correct sum or difference.

Adding Polynomials

The easiest type of problem is one where all terms being added are positives.  The examples below show how to add binomials vertically.


Rewriting the problems vertically is a trick that can help organize each term and make sure that youare adding the correct terms.  In the following problems, the polynomials that are being added have some terms that cannot be added to anything else.  In these problems, simply bring down the terms with no match and include them in the answer.  Remember, you may only add like terms.


In the second problem above, notice that x4 + 3x4 = 4x4.  The first x4 lacks a coefficient, while the second one has a coefficient of 3.  Any time a variable term doesn’t have a coefficient, always assume that coefficient is a 1.



All the problems you have seen thus far have involved polynomials with positive terms.  The exact same rules apply if you have negative terms.  Just remember that when adding a positive and a negative you subtract the numbers and keep the sign of the number with the largest absolute value.




One final example contains two polynomials that are not in standard form.  To do problems of this type, simply reorder the polynomials to put them in standard form, then add the terms one by one.





Try It

1)  (11x2 – 5x + 14) + (3x2 + 6x + 5)

2)  (2x3 + 14x2 + 3x + 8) + (-2x3 – 10x2 + 6x – 4)

3)  (5x5 + 7x3 – 11x2 + 9x + 13) + (-7x5 – 3x4 + - 2x3 + 3x2 – 3x)

4)  (2x2 – 10x + 7) + (-x + 3x2 + 5)

5)  (14 + 4x2 + 8x3 – 5x) + (18x + 4 – 4x3 – 8x2)








1)  14x2 + x + 19

2)  4x2 + 9x + 4

3)  -2x5 – 3x4 + 5x3 – 8x2 + 6x + 13

4)  5x2 – 11x + 12

5)  4x3 – 4x2 + 13x + 18





Related Links:

Didn't find what you were looking for in this lesson?  More information on polynomials can be found at the following places:

Resource Page

Related Lessons


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