Differentiation

Let $\mathbb{R}$ denote the set of all real numbers. Consider the polynomial function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by

\(f(x)=\frac{d^{10}}{d x^{10}}\left(\left(x^2-1\right)^{10}\right), \quad \text { for all } x \in \mathbb{R}\)

Here $\frac{d^{10}}{d x^{10}}\left(\left(x^2-1\right)^{10}\right)$ is the $10^{\text {th }}$ order derivative of the function $\left(x^2-1\right)^{10}$.

Then which of the following statements is (are) TRUE ?