Characteristics of Polynomials

Determine which of the following polynomial functions is even, odd or neither.

(a) f(x) = 3x^4 - 2x + **1**...The answer is neither. BUT what makes it neither?

(b) f(x) = 3x^9 - 2x^5 + **1**...The answer is neither. BUT what makes it neither?

Does the constant **1** make the two functions above neither?

Even functions have even powers and odd functions have odd powers. Am I right?

Neither functions involve functions that have both even and odd powers. Am I right?

I am still unclear about the "neither" concept.

To me, function (a) is even and and function (b) is odd.

The textbook tells me that I am wrong.

Can someone explain in simple terms this "neither" concept?

I want to fully grasp all basic concepts of precalculus before starting calculus 1 next semester.

By the way, I passed precalculus last semester with an A minus thanks to the wonderful math teachers on this website.