#### Answer

It is a polynomial.
Degree: 4
Leading term: $5x^4$
Constant: $\frac{1}{2}$
$5x^4- \pi x^3+.5$

#### Work Step by Step

By definition, a polynomial is a function containing only terms where x is raised to a positive, integer power or constants. x is raised to the third power, x is raised to the fourth power, and $\frac{1}{2}$ is a constant, so we see that it is a polynomial. The degree is equal to the exponent of the term with the highest exponent, so the degree is 4. The term that has the highest degree, $5x^4$, is always the leading term. Finally, $\frac{1}{2}$ is a constant.