Commands for compliation and execution:

Problem 1:
g++ -ansi -pedantic -Wall main_1.cxx polynomial_1.cxx -o polynomial
./polynomial

Problem 2:
g++ -ansi -pedantic -Wall main_2.cxx -o polynomial
./polynomial

Comments:
-Coding this way does not, in fact, have a learning curve. It is still hard.
-Part 1, after much trial and error, finally worked once I reorganized and figured out that faulty math was the main culprit to things not compiling.
-Part 2 was made easier by Part 1, as it was mostly light editing