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Hello - I'm new to SAGE, so trying to get to grips with the basics!

I have a polynomial $f = x^{2}((x+\frac{1}{x})^{2} - 1)$. I would like to be able to do to things:

1) See $f$ in the form $\beta(x - \alpha_1)(x-\alpha_2)(x-\alpha_3)(x-\alpha_4)$

2) Know the value of $\beta (\prod_i \alpha_i)$

Using

f.factor

f.roots

Does not give me the linear factorisation, nor can I see a simple way of getting the product of the roots.

In the long term I'm hoping to do this for polynomials of larger degree, so any advice would be great!