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Example:Dividing Polynomials

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In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.

The quotient and remainder can then be determined as follows:

1.  Divide the first term of the numerator by the highest term of the denominator. Place the result above the bar.


2.  Multiply the denominator by the result just obtained (the first term of the eventual quotient). Write the result under the first two terms of the numerator.


3.  Subtract the product just obtained from the appropriate terms of the original numerator, and write the result underneath. This can be tricky at times, because of the sign. Then, "bring down" the next term from the numerator.


4.  Repeat the previous three steps, except this time use the two terms that have just been written as the numerator.


Repeat step 4. Till there is nothing to "pull down". (Our solved example in mathguru.com uses this concept).

The polynomial above the bar is the quotient, and the number left over is the remainder.




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.