Question

Is `f(x)= -3x^4sqrtx+13x^2-5x` a polynomials?

Answer 1

It is not a polynomial in `x` since not all of the powers of `x` are integers. It is a polynomial in `sqrt(x)`.

Explanation:

`sqrt(x) = x^(1/2)` is a non integer power of `x` so this is not a polynomial in `x`.

It is a polynomial in `sqrt(x)`...

If you put `y = sqrt(x)`, then

`f(x) = -3y^9+13y^4-5y^2` with the restriction `y >= 0`.

This is a polynomial in `y`.