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Author: Nate Muckley
##### Description:

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.

(more)

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Tutorial

## Polynomials

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

Example:

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.

So:

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. (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

5x3 + 7x2 + 4x + 10

## Subtraction

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!