SOLUTION: Hello, Could I get some help with an algebra problem? Algebra problem: (2 - x + 2x^2 - x^3)/(x - 2) I keep getting - x^2 (x -2) but the book states: -(x^2 + 1) M

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Question 1106038: Hello,
Could I get some help with an algebra problem?
Algebra problem:
(2 - x + 2x^2 - x^3)/(x - 2)
I keep getting - x^2 (x -2)
but the book states:
-(x^2 + 1)
My procedure is:
(2 - x + 2x^2 - x^3)/(x - 2) -->
(-x^3 + 2x^2 -x +2)/(x -2) -->
- (x^3 - 2x^2 + x - 2)/(x -2) -->
- (x^3 - 2x^2) (x - 2) - grouping -->
- x^2 (x - 2) (x - 2)/(x - 2)
cancel the (x - 2) and I get:
- x^2 (x - 2)
Does anyone know where I made my error?

Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
(2 - x + 2x^2 - x^3)/(x - 2)
I keep getting - x^2 (x -2)
but the book states:
-(x^2 + 1)
My procedure is:
(2 - x + 2x^2 - x^3)/(x - 2) -->
(-x^3 + 2x^2 -x +2)/(x -2)
=
=
=
=
===========================
- (x^3 - 2x^2 + x - 2)/(x -2) -->
- (x^3 - 2x^2) (x - 2) - grouping -->
- x^2 (x - 2) (x - 2)/(x - 2)
cancel the (x - 2) and I get:
- x^2 (x - 2)
Does anyone know where I made my error?

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The other tutor showed how to get the book's answer; he didn't point out where your error was....

Here is what you show...

(2 - x + 2x^2 - x^3)/(x - 2) original problem...

(-x^3 + 2x^2 -x +2)/(x -2) put in standard form (decreasing powers) ... good

- (x^3 - 2x^2 + x - 2)/(x -2) factor out the -1 to make the leading coefficient positive... okay, but not necessary

- (x^3 - 2x^2) (x - 2) - grouping NO. You have changed addition/subtraction to multiplication. Your expression here should be
- (x^3 - 2x^2) - (x-2)

- x^2 (x - 2) (x - 2)/(x - 2) now of course this is invalid....

I don't remember what the other tutor showed in his response, so I will show how I would do this...