Question

What is it I'm confused. Its either 2,3,-9,7,or 4.

Answer 1

so, it boils down to the definition of a polynomial.

a polynomial is just a term with coefficients and variables at whatever power, however, it cannot be a rational, namely a fraction.

if we choose any positive exponent or that "x", we'll....let's pick say 3 and 7 just so you see what happens.

`\bf 3x^4+4x^2-9x^{\setlength{\fboxsep}{1pt} -\boxed{\text{\tiny 3}}}+2\implies 3x^4+4x^2-9\cdot \cfrac{1}{x^3}+2\impliedby \textit{a fraction} \\\\\\ 3x^4+4x^2-9x^{\setlength{\fboxsep}{1pt} -\boxed{\text{\tiny 7}}}+2\implies 3x^4+4x^2-9\cdot \cfrac{1}{x^7}+2\impliedby \textit{another fraction}`

so, if we give it any positive exponent, we'll end up with a rational, however if we give it a negative, like say -9,

`\bf 3x^4+4x^2-9x^{\setlength{\fboxsep}{1pt} -\boxed{\text{\tiny -9}}}+2\implies 3x^4+4x^2-9\cdot x^(+9)+2 \\\\\\ 3x^4+4x^2-9x^9+2\impliedby \textit{not a fraction, thus a polynomial}`