SOLUTION: please explain how to do long division (b^3-27)/(b-3)= and then how do I check this

Question 427656: please explain how to do long division
(b^3-27)/(b-3)=
and then how do I check this
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
(b�-27)/(b-3)=



Write b� - 27 as b� + 0b� + 0b - 27 

Write this:

                        
b - 3)b� + 0b� + 0b - 27
      
b� divided by b give b�

            b�          
b - 3)b� + 0b� + 0b - 27
     
b� times -3 gives -3b

            b�          
b - 3)b� + 0b� + 0b - 27
         - 3b�

b� times b gives b�

            b�          
b - 3)b� + 0b� + 0b - 27
      b� - 3b�

Draw a line:

            b�          
b - 3)b� + 0b� + 0b - 27
      b� - 3b�

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

            b�          
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b�

Bring down the + 0b

            b�          
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b

3b� divided by b give 3b

            b� + 3b     
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b

3b times -3 gives -9b

            b� + 3b     
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
               - 9b

3b times b gives 3b�

            b� + 3b     
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b

Draw a line:

            b� + 3b     
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b

Subtract 3b� - 3b�, that gives 0 so we don't write anything
under that.  then 0b minus -9b is really 0b+9b or 9b

            b� + 3b     
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b

Bring down the - 27

            b� + 3b     
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b - 27

9b divided by b give 9

            b� + 3b + 9
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b - 27
 
9 times -3 gives -27

            b� + 3b + 9
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b - 27
                    - 27

9 times b gives 9b

            b� + 3b + 9
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b - 27
                 9b - 27

Draw a line:

            b� + 3b + 9
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b - 27
                 9b - 27

Subtract 9b - 9b, that gives 0 so we don't write anything
under that.  then -27 minus -27 is really -27+27 or 0, so
the remainder is 0:

            b� + 3b + 9
b - 3)b� + 0b� + 0b - 27
      b� - 3b�
           3b� + 0b
           3b� - 9b
                 9b - 27
                 9b - 27
                       0

That's it.  The answer, or quotient, is b� + 3b + 9

Edwin

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