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Adding and Subtracting Polynomials!

Adding and Subtracting Polynomials!

Author: Nate Muckley

Learn to add and subtract polynomials.

Get the definition of a polynomial, and then learn to use polynomials in addition and subtraction. Colored pictures and easy descriptions help make the concept understandable.

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POLYNOMIALS are expressions with multiple terms that are raised to a positive, whole number power.


x+ 3x + 4

     This is a polynomial, because the first x is raised to the second power, the second x is raised to the first power, and you can't see the third x, because it is raised to the zero power.  But it's much easier

     The x2, 3x, and 4 in the eqution, are all TERMS. A term is a part of a polynomial.  

     Terms are separated by + and - but NEVER by multiplication or division!

     A term by itself is not a polynomial.  "Poly" is a Greek prefix meaning "many," so you must have many terms to make a polynomial.

    Another important word is DEGREE. The degree of the polynomial is the highest  exponent to which it is raised.


2x3 + 7x2 - x + 4                         is a third degree polynomial with 4 terms.


x3 - 7x + 9                                    is a third degree polynomial with 3 terms.


x4 + 4x                                         is a fourth degree polynomial with 2 terms.


x-3 + 2x + 5       is NOT a polynomial: the x is raised to a negative exponent.


 x3 - 7x2/3 - x2    is NOT a polynomial: The 7x is being raised to the 2/3 power.



     Polynomials can be added and subtracted to each other.  In order to do so, you must combine like terms.  Then add or subtract the individual terms.

Then you put your terms together to get your answer.


Here's an example of addition:

(4x3 + x2 + 5x) + (x3 + 6x2 - x + 10)

Now put like terms together.  If there are no like terms to match up with a particular term, it remains as it is.

(4x3 + x3)     +     (x2 + 6x2)     +     (5x - x)     +     (10)

               5x3              +           7x2            +         4x         +      10

so the final answer =

5x3 + 7x2 + 4x + 10


Subtraction is similar to addition, but you need to distribute the negative when you combine.

Here are more problems, scroll down for the answers.

(3x4 - 10x3 + 2x -17) - (12x4 + 3x3 -x2 + 2x - 22) = ?


(4x4 - 6x3 + 3x -7) + (-x4 + 7x3 + 2x2 + 1) = ?


Tricky:     (4x3 + 6y2 + x + y) + (y3 - 4y2 + 3) - (x3 - 2x2 + 2) = ?

Remember: X and Y are NOT like terms!























-9x4 - 13x3 + x2 + 5

3x4 + x3 + 5x - 6

3x3 + 3y3 + 2x2 + 2y2 + x + y + 1