Question:Divide `2x^2` + 7x + 6 by x+2 

x + 2)`2x^2` + 7x+6( 2x + 3
      `2x^2` + 4x
       ------------
              3x + 6
              3x + 6
             ----------
                 0

The quotient is 2x + 3

Question:Divide `4x^4` - `3x^3` +  `2x^2` -5x +6 by `x^2` - 3x - 1 

`x^2` - 3x - 1 ) `4x^4` -  `3x^3` + `2x^2` - 5x + 6 ( `4x^2` + 9x + 33
                       `4x^4` - `12x^3` -  `4x^2` 
                       ---------------------------------
                                    `9x^3` +  `6x^2` - 5x
                                    `9x^3` - `27x^2` - 9x
                                    -----------------------------
                                                  `33x^2` + 4x +   6
                                                  `33x^2` - 99x - 33
                                                  ---------------------
                                                               103x + 39 

The quotient is `4x^2` + 9x + 33; the reminder is 103x + 39.

Question:Divide `x^3` + 8 by x + 2. 

 `x^2` - 2x + 4
x + 2 ) `x^3`             + 8(
          `x^3` + 2`x^2`
           -----------------
                     - 2`x^2`
                     - 2`x^2` - 4x
                    -----------------
                                     4x + 8
                                     4x + 8
                                     --------

The quotient is `x^2` - 2x + 4.