Question

Is `f(x)=(2x^3-5x^5-2)/(9x^2+9)` a polynomials?

Answer 1

No, the ratio is not a polynomial. (The numerator and denominator separately are polynomials.)

Explanation:

A polynomial (in one variable) consists of terms (things added together), each of which is a constant (a number) times the variable raised to some positive whole number power (or just a constant alone).

`2x^3-5x^5-2` is an example of a polynomial.
The terms are `2x^3` and `-5x^5` and `-2`.
Actually, I've listed the terms with non0zero coefficient. If we want, we can also insert "terms" `0x^4` and `0x^2` and so on. (And even `0x^7` if there is a reason to add that term.)

The expression `(2x^3-5x^5-2)/(9x^2+9)` is called a Rational expression.

(And the function `f(x) = (2x^3-5x^5-2)/(9x^2+9)` is called a Rational Function.)