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

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Answer 1 · 2015-06-13T22:12:31

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

$sqrt(x) = x^(1/2)$ 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 $y$ .

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