Consider rational functions whose denominators contain either distinct linear factors or a repeated linear factor.
(a) Describe the difference in the algebraic form used for decomposition when the denominator is (i) (x−a)(x−b)(x−c) and (ii) (x−a)3.
(b) Give a brief reason why a denominator of type (ii) introduces three unknown constants in the decomposition, whereas type (i) introduces only one constant per factor.
(c) Explain why the decomposition step is preceded by checking whether the given rational function is proper.