c
(c)  \({{3{x^3} - 8{x^2} + 10} \over {{{(x - 1)}^4}}} = {A \over {x - 1}} + {B \over {{{(x - 1)}^2}}} + {C \over {{{(x - 1)}^3}}} + {D \over {{{(x - 1)}^4}}}\)

==>\(3{x^3} - 8{x^2} + 10 = A{(x - 1)^3} + B{(x - 1)^2} + C(x - 1) + D\)

Equating coefficients of different powers of \(x\), \(3 = A\)

\( - 8 = - 3A + B \Rightarrow B = 1\)

\(0 = 3A - 2B + C \Rightarrow C = - 7\)

\(10 = - A + B - C + D \Rightarrow D = 5\)

\(\therefore\) Given expression

= \({3 \over {x - 1}} + {1 \over {{{(x - 1)}^2}}} - {7 \over {{{(x - 1)}^3}}} + {5 \over {{{(x - 1)}^4}}}\).