A polynomial is any expression that has variables (such as x) and coefficients (the things in front of the variable; i.e. in 5x, 5 is the coefficient), that involves only the operations of addition, subtraction, multiplication, and non-negative exponents. A few examples are

,

, and

.
Some examples of non-polynomials include

, x+1, x+x+y-y. If you need any more help or examples, I can provide more.