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

Jun 13, 2015

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:

$\sqrt{x} = {x}^{\frac{1}{2}}$ 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

$f \left(x\right) = - 3 {y}^{9} + 13 {y}^{4} - 5 {y}^{2}$ with the restriction $y \ge 0$.

This is a polynomial in $y$.