SOLUTION: Perform long division: {{{(x - (1/3)x^4 + 2x^3 + 2x^2)/(x -6)}}}

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Question 154557: Perform long division:


Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Perform long division:
x - 1/3x^4 + 2x^3 + 2x^2 -x -6
-------------------------------------------
Using synthetic division:
1)....(1/3)...2....2....-1....-6
.........1/3...7/3..13/3..10/3..|.-8/3
Quotient: (1/3)x^3 + (7/3)x^2 + (13/3)x + (10/3)
Remainder: -8/3
========================
Cheers,
Stan H.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Stanbon's solution is wrong.
Correct solution by Edwin:


I can't tell whether the divisor is  or 
so I'll do it both ways.  With divisor 

÷

Rearrange the numerator in descending order:

÷

There is a missing constant term on the right end
so we put 0

÷


             (-1/3)x³ + 0x² + 2x + 13 
     --------------------------------
x - 6) (-1/3)x4 + 2x³ + 2x² +  x +  0
       (-1/3)x4 + 2x³
       --------------
                  0x³ + 2x²
                  0x³ + 0x²
                  ---------
                        2x² +  x  
                        2x² -12x
                        --------
                             13x +  0
                             13x - 78
                             --------
                                   78

Answer:   

--------------------------------

With divisor 

÷

Rearrange the numerator in descending order:

÷

There is a missing constant term on the right end
so we put 0

÷


               (1/3)x³ -  4x² +  22x - 133 
      ------------------------------------
-x - 6) (-1/3)x4 + 2x³ +  2x² +    x +   0
        (-1/3)x4 - 2x³
       --------------
                   4x³ +  2x²
                   4x³ + 24x²
                  ---------
                        -22x² +    x  
                        -22x² - 132x
                        ------------
                                133x +   0
                                133x + 798
                             -------------
                                      -798 

Answer:   





Edwin

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