- #1

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## Homework Statement

The following is a worked example, I circled around the part which I couldn't follow:

http://img15.imageshack.us/img15/161/untitleou.jpg [Broken]

## Homework Equations

## The Attempt at a Solution

To begin with, I can't understand why they wrote:

[tex]x-1 = \frac{1}{3}(x^3-x^2+2x-2)-\frac{1}{3}(x+1)(x^2-2x+1)[/tex]

(or [tex]3x-3 = (x^3-x^2+2x-2)-(x+1)(x^2-2x+1)[/tex])

What formula/theorem were they using here? I can't follow what is done here.

P.S. On the top it says [tex]gcd(2x^3+x^2-2x-1, x^3-x^2+2x-2)= x-1[/tex], but it previously said "the last non-zero remainder is a gcd". And when the Euclidean algorithem was applied we found that the last non-zero remainder is

**3x-3**NOT

**x-1**.

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