Polynomial Definition

Can you explain the polynomial definition?

 

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") , so it says "many terms".

or
-a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx^2)

a polynomial can have constants, variables and exponents, but never division by a variable

constants (like 3, -20, or ½)
variables (like x and y)
exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed
that can be combined using addition, subtraction, multiplication and division
except division by a variable (so something like 2/x is right out)

 

Ok. Cool. I just wanted to make sense of the long general formula that represents a polynomial in most algebra textbooks.