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

$$f(x)=\dfrac{d^{10}}{dx^{10}}\big((x^2-1)^{10}\big),\qquad\text{for all }x\in\mathbb{R}.$$

Here $$\dfrac{d^{10}}{dx^{10}}\big((x^2-1)^{10}\big)$$ is the $$10^{\text{th}}$$ order derivative of the function $$(x^2-1)^{10}$$.

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