problem to determine the chromatic polynomial of a graph for a homework graph theory, I'm asked to determine the chromatic polynomial of the following graph
this is my  thread in another post:
https://stackoverflow.com/questions/5724167/problem-to-determine-the-chromatic-polynomial-of-a-graph
For the Descomposition Theorem of Chromatic Polynomials. if G=(V,E), is a connected graph and e belong E 
P (G, λ) = P (Ge, λ) -P(Ge', λ)

When calculating chromatic Polynomials, i shall place brackets about a graph to indicate its chromatic polynomial. removes an edge any of the original graph to calculate the chromatic polynomial by the method of decomposition.
 P (G, λ) = P (Ge, λ)-P (Ge ', λ) = λ (λ-1) ^ 3 - [λ (λ-1) (λ^2 - 3λ + 3)]

But the response from the answer key and the teacher is:
P (G, λ) = λ (λ-1)(λ-2)(λ^2-2λ-2)

I have operated on the polynomial but I can not reach the solution that I ask .. what am I doing wrong?

I think what you need in your answer is $\lambda (\lambda- 1)^4$ for the polynomial of Ge.  The 5-cycle with one edge removed is a path of five vertices.  $\lambda$ choices for the first, and $(\lambda - 1)$ choices for the other 4.
