How to apply polynomial long division to $x^3/(x^2+3x+2)$ So I have a basic question. I needed to simplify this expression 
$$\frac{x^{3}}{x^{2} +3x +2}$$
I was to do a polynomial long division in order to simplify it, but I still do not understand how they reached this next expression (I know it can be more simplified)
$$\frac{x^{3}}{x^{2} +3x +2}= x-3 + \frac{7x+6}{x^{2} +3x +2}$$
What was divided by what?
Any help would be appreciated. Thanks in advance!!
 A: Long division of polynomials is done in the same way as ordinary long division, except there is no carry.  Because of this, it is best to reverse the sign of what is written in the 'take away bit', and do straight additions.  
When one multiplies down a number into the subtraction area, the sign is changed to make the additions and subtractions happen easier.  So the first row is transferred as -1 * 1,3,2 even though a +1 results in the answer.
                            1 -3  .  7  -27
                ----------------------------
        1  3  2 )     1  0  0  0  .
                     -1 -3 -2
                      --------
                       -3  -2
                        3   9   6 .
                       ------------
                        0   7  -6   <--  desired remainder
                           -7  -21 -14
                           -----------
                               -27 -14
                                27  81  54
                                    ------
                                    67 -55

The answer is variously $(x-3)(x+3+2) + (7x-6)$, or $(x+3+2)(x-3+7x^{-1}-27x^{-2}\dots$
A: Simply, divide with remainder $x^3$ by $x^2 + 3 x + 2$. You get
$$
x^3 = (x^2 + 3 x + 2) (x - 3) + (7 x + 6).
$$
A: $$\frac{x^3}{x^2+3x+2} = \frac{x(x^2+3x+2)-3x^2-2x}{x^2+3x+2} = x - \frac{3(x^2+3x+2)-7x-6}{x^2+3x+2}=x-3+\frac{7x+6}{x^2+3x+2}.$$
A: You're right to use long division to simplify this expression. I think where you got stuck was knowing how to set up the initial long division. You are dividing $ x^{3}$ by ($ x^{2} + 3x + 2$), so the $ x^3$ goes underneath the long division bar, but you MUST put zero placeholder terms for any terms that are missing. This means you actually need to write $x^3 + 0x^2 + 0x + 0$ as your dividend underneath the division line.  Then your divisor of course you write the left of the division bar, which is $ x^{2} + 3x + 2$. You then carry out normal long division steps. If you want more help with long division of polynomials, especially for problems with missing terms in the polynomial, here's a video that explains it: http://www.youtube.com/watch?v=Ih1wb6AxhMI  Good luck!
