Use of Division in Factoring - Polynomials by binomials

[saramissy51]

I am having a problem understanding the use of division in the process of factoring polynomial's with a given binomial. An example question is as follows:

Dividing the polynomial x 3rd power plus 2x 2nd power minus 5x-6 by the binomial of x+1.

The example I'm looking at does not make sense to me in the fact that answer according to my text book is x to the second power + x -6. (Sorry, I do not know how to do superscript in this system). Can you put an explanation in layman's terms instead of mathmatical terms that I may understand better?

Thank you,

 

[skeeter]

not much to explain, it's just straightforward polynomial long division ...

      x^2 + x - 6
    -------------------------
x+1 | x^3 + 2x^2 - 5x - 6
      x^3 + x^2
     ------------------------
            x^2 - 5x - 6
            x^2 + x
           ---------------
                 -6x - 6               
                 -6x - 6
                 ----------

maybe you need to see a lesson ...

http://www.purplemath.com/modules/polydiv2.htm

note that this may also be accomplished using synthetic division ...

http://www.purplemath.com/modules/synthdiv.htm