I won't give the right answers here. If you want to know the right answers, come to see me.
21.3.01 You probably shouldn't check it by hand, because you have to explain why the period is the maximum. Read ahead (Section 21.7) for a more mathematical argument.
21.10.04 I'm giving one here, there is another one out there for you to find.
x^6+x^3+1
21.10.05 I'm sensing most of you gave it up when sighting this one. Here is one primitive octic for your enjoyment.
x^8+x^7+x^5+x^3+1
You won't get (full) credit just by listing the polynomial, though.