If f (x) = 2x² + 2 and g(x) = x³ + 2x + 1 demonstrate that functions resulting from the following are also polynomial. State the order of the resulting polynomial function in each case.

a. f(x) + g(x)

b. f(x) × g(x)

c. (f ◦ g)(x)

d. (g ◦ f )(x)