#### Answer

The given function $f\left( x \right)=\frac{{{x}^{2}}+7}{3}$ is a polynomial with degree $2$.

#### Work Step by Step

A function is said to be a polynomial function if
$g\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+\cdots +{{a}_{2}}{{x}^{2}}+{{a}_{1}}x+{{a}_{0}}$ ,
Where ${{a}_{n}},{{a}_{n-1}},\ldots ,{{a}_{2}},{{a}_{1}},{{a}_{0}}$ are any real numbers with ${{a}_{n}}\ne 0$ and n is any non-negative integer.
The function g(x) is called a polynomial function of degree n; its coefficient is called the leading coefficient.
Now, the given function $f\left( x \right)=\frac{{{x}^{2}}+7}{3}$ can be simplified to $f\left( x \right)=\frac{1}{3}{{x}^{2}}+\frac{7}{3}$. The function satisfies all the conditions to be a polynomial; hence, this function is a polynomial and since the highest power of f(x) is 2 then the degree of the polynomial is 2.
Hence, the given function $f\left( x \right)=\frac{{{x}^{2}}+7}{3}$ is a polynomial with degree 2.