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
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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
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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)x� + 0x� + 2x + 13 -------------------------------- x - 6) (-1/3)x⁴ + 2x� + 2x� + x + 0 (-1/3)x⁴ + 2x� -------------- 0x� + 2x� 0x� + 0x� --------- 2x� + x 2x� -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)x� - 4x� + 22x - 133 ------------------------------------ -x - 6) (-1/3)x4 + 2x� + 2x� + x + 0 (-1/3)x4 - 2x� -------------- 4x� + 2x� 4x� + 24x� --------- -22x� + x -22x� - 132x ------------ 133x + 0 133x + 798 ------------- -798 Answer: Edwin