This one is not so bad.
1)Let be an -th degree* polynomial function such that . Define the function as:
. Show that .
2)What is the least number of moves that a player can make to give a checkmate?
*)And the condition that because the degree of a zero polynomial is not defined. The degree of a constant non-zero polynomial is defined to be zero. However, some authors in field theory differ on their defintions of the degree of the zero polynomial. Some define it to be and other to be . The way I learned it the zero polynomial had an undefined degree. This is why I make such a comment just in case you spotted the mistake in my first sentence.