are either of these polynomials?
*f(x)=x^3-11x^2+3^x

*f(x)=2x^3-5x^5-2/9x^2+9

Question

are either of these polynomials?
*f(x)=x^3-11x^2+3^x

*f(x)=2x^3-5x^5-2/9x^2+9

anonymous · Answer

not sure if a polynomial can a variable for an exponent

anonymous · Answer

A polynomial is a polynomial if and only if the co-efficients are all real and all the exponents of the terms are real numbers and positive.
So for example, $f(x)=x^3-11x^2+3^x$ Is NOT a polynomial because the third term has a exponent which is not a real number, But a variable.

anonymous · Answer

Just a question, is the second one, $f(x)=2x^3-5x^5-\frac{2}{9x^2}+9$ ?

anonymous · Answer

what about if there was a fraction with a variable on the side?

anonymous · Answer

like the "co-efficient" is the fraction, or the "exponent" is the fraction or the variable is the fraction?

anonymous · Answer

like for ex: (2/9)x^2 .

anonymous · Answer

That is OKAY. Because $\frac{2}{9}$, Though it is a fraction represents a number (0.22222...) So it is a valid co-efficient.

anonymous · Answer

Think about it like this. Would $(\frac{2}{9}x^2)$ Look more "polynomial-ish" if it was $(0.222x^2)$?

anonymous · Answer

cool thank you!