Find p(0), p(1) and p(2) for the polynomial, p(x) = (x - 1)(x + 1).

Given: p(x) = (x - 1)(x + 1)

For p(0), substituting x = 0 in the given expression, we get:

$\begin{array}{c}\Rightarrow \mathrm{p}\left(0\right)=(0-1)\text{ (0+1)}\\ \\ \Rightarrow \mathrm{p}\left(0\right)=(-1)\text{ (1)}\\ \\ \Rightarrow \mathbf{p}\mathbf{\left(}\mathbf{0}\mathbf{\right)}\mathbf{=}\mathbf{\text{- 1}}\end{array}$    

Hence, the value of the polynomial p(x) at x = 0 is - 1.

For p(1), substituting x = 1 in the given expression, we get:

$\begin{array}{c}\Rightarrow \mathrm{p}\left(1\right)=(1-1)\text{ (1+1)}\\ \\ \Rightarrow \mathrm{p}\left(1\right)=\left(0\right)\text{ (2)}\\ \\ \Rightarrow \mathbf{p}\mathbf{\left(}\mathbf{1}\mathbf{\right)}\mathbf{=}\mathbf{0}\end{array}$

Hence, the value of the polynomial p(x) at x = 1 is 0.

For p(2), substituting x = 2 in the given expression, we get:

$\begin{array}{c}\Rightarrow \mathrm{p}\left(2\right)=(2-1)\text{ (2+1)}\\ \\ \Rightarrow \mathrm{p}\left(2\right)=\left(1\right)\text{ (3)}\\ \\ \Rightarrow \mathbf{p}\mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{=}\mathbf{3}\end{array}$

Hence, the value of the polynomial p(x) at x = 2 is 3.

Thus, the values of the polynomial $\mathbf{p}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{1}\mathbf{)}\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{1}\mathbf{)}$ at x = 0, 1, and 2 are - 1, 0, and 3.