(abstract algebra) Let F be a field. Suppose f(x), g(x), h(x) ∈F[x]. Show that the following properties hold:
(a) If g(x)|f(x) and h(x)|g(x), then h(x)|f(x).
(b) If g(x)|f(x), then g(x)h(x)|f(x)h(x).
(c) If h(x)|f(x) and h(x)|g(x), then h(x)|f(x) ± g(x).
(d) If g(x)|f(x) and f(x)|g(x), then f(x) = kg(x) for some k ∈ F\ {0}
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