Hi, there--

The problem:
Simplify (x^5-x^3+2x-9+5)/(x+2) by dividing.

A solution:
We can solve this using long division (just like in fifth grade, except you have variables.)
Remember to keep everything lines up and make sure to only add and subtract like terms.

Notice that 
x^5-x^3+2x-9+5 = x^5 + 0x^4 - x^3 + 0x^2 + 2x -4
 

          x^4 - 2x^3 + 3x^2 - 6x + 14
         ___________________________________
x+2 ) x^5 + 0x^4 - x^3 + 0x^2 + 2x - 4
         x^5 + 2x^4
         ----------
                - 2x^4 -   x^3
                - 2x^4 - 4x^3
                ------------
                               3x^3 + 0x^2
                               3x^3 + 6x^2
                               -----------
                                         - 6x^2 + 2x
                                         - 6x^2 -12x
                                         -----------
                                                      14x - 4
                                                      14x + 28
                                                      --------
                                                             - 32

The quotient is x^4 - 2x^3 + 3x^2 - 6x + 14 with a remainder of -32.
You can also write this as:
x^4 - 2x^3 + 3x^2 - 6x + 14 - 32/(x+2)  

Feel free to email me if you have questions about this solution.

Ms.Figge
math.in.the.vortex@gmail.com