This answer gives a really great explanation of why partial fraction decomposition works. However, the explanation implies that rational functions can be decomposed into a sum of fractions plus a polynomial. Yet, when decomposing rational functions we don't seem to account for the potential polynomial term. Why?
2026-03-30 16:58:24.1774889904
Partial fraction decomposition and polynomials?
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Sure we do, if the degree of the numerator is at least the degree of the denominator. We do long division first to recover the polynomial part.