For which polynomials does limit (x->0) exist for W(x)/ln(1 - x^2)

[anth]

For which real polynomials W
lim x to 0 W(x)/ln(1 - x^2)
exist and is real number?

 

[Deleted member 4993]

For which real polynomials W
lim x to 0 W(x)/ln(1 - x^2)
exist and is real number?

What are your thoughts?
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[anth]

I have to characterize all polynomials for which this limit is a real number.

. . . . .\(\displaystyle \displaystyle \lim_{x \rightarrow 0}\, \dfrac{W(x)}{\log(1\, -\, x^2)}\)

I have no idea. This natural logarithm spoils everything.