I have a problem that asks me to find a polynomial $P(x)$ so that $P(3)$ is 9.

Now I can say with certainty that $P(x)$ can be $x^2$. This is a second degree polynomial.

But what about functions such as $\frac{1}{x^2+3}$, are these not polynomials? If not, why?

P.S. I seem to be having troubles with the math tags. Some help on that would be appreciated as well.