3. Provide an example of a polynomial $P(x)$ of degree 2001 for which the identity

$$
P(x)+P(1-x)=1
$$

holds.
3. Let, for example, $P(x)=\left(x-\frac{1}{2}\right)^{2001}+\frac{1}{2}$. Then

$$
P(1-x)=\left(\frac{1}{2}-x\right)^{2001}+\frac{1}{2}=-\left(x-\frac{1}{2}\right)^{2001}+\frac{1}{2}
$$

therefore $P(x)+P(1-x)=1$.