Simplify characteristic equation

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I have a rather unwieldy symbolic expression of the form f(x) = 0, where the left hand side is a (low-degree) polynomial in x. I need to extract the constant term and the coefficients of a few powers of x in f(x). If I try to simplify either f(x) itself or each coefficient, Sage runs out of memory (even after increasing the Maxima heap size) or doesn't ever seem to terminate. Is there something I can do that takes advantage of the special form of the equation to simplify the coefficients?