Answer the following questions about rational functions with repeated linear factors.
a. (i) Define a proper rational function.
b. (ii) Write the most general form in which a rational function (x−3)3P(x) with degP(x)≤2 can be expressed when it is split into simpler fractional terms.
c. (iii) State any two algebraic checks that must be performed before carrying out such a decomposition.