I cheated and went to wikipedia but the definition is good
"a polynomial is an expression of finite length constructed from variables (also called indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents."
pay particular attention to the the very last qualifier of the quote
in a) the exponents on you x variable are 5, and 1. both integers
in b) the exponents on the c variable are 2, -1. both integers, but one negative. this does not fit the description of a polynomial