SOLUTION: need to know how to do long division (x^3+2x^2+3x-6)/(x-1) Please show how to do this

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Question 427653: need to know how to do long division
(x^3+2x^2+3x-6)/(x-1)
Please show how to do this
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
(b³-27)/(b-3)=
(x^3+2x^2+3x-6)/(x-1) 


 Write this:

                       
x - 1)x³ + 2x² + 3x - 6
      
x³ divided by x give x²

            x²         
x - 1)x³ + 2x² + 3x - 6
     
x² times -1 gives -x²

            x²         
x - 1)x³ + 2x² + 3x - 6
         -  x²

x² times x gives x³

            x²         
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²

Draw a line:

            x²         
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
     
Subtract x³ - x³, that gives 0 so we don't write anything
under that.  then 2x² minus -x² is really 2x²+x² or 3x²

            x²         
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x²

Bring down the + 3x

            x²         
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x


3x² divided by x give 3x

            x² + 3x    
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x


3x times -1 gives - 3x

            x² + 3x    
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
               - 3x 

3x times x gives 3x²

            x² + 3x    
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x 

Draw a line:

            x² + 3x    
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x 


Subtract 3x² - 3x², that gives 0 so we don't write anything
under that.  then 3x minus -3x is really 3x+3x or 6x

            x² + 3x    
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x

Bring down the - 6

            x² + 3x    
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x - 6

6x divided by x give 6

            x² + 3x + 6
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x - 6
 
6 times -1 gives - 6

            x² + 3x + 6
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x - 6
                    - 6
6 times x gives 6x

            x² + 3x + 6
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x - 6
                 6x - 6

Draw a line:

            x² + 3x + 6
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x - 6
                 6x - 6

Subtract 6x - 6x, that gives 0 so we don't write anything
under that.  then -6 minus -6 is really -6+6 or 0, so
the remainder is 0:

            x² + 3x + 6
x - 1)x³ + 2x² + 3x - 6
      x³ -  x²
           3x² + 3x
           3x² - 3x
                 6x - 6
                 6x - 6
                      0 
That's it.  The answer, or quotient, is x² + 3x + 6

Edwin
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