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# Find p(0), p(1)and p(2) for each of the following polynomials :i)$$p(y) = y^2 -y + 1$$ii)$$p(t) = 2 + t + 2t^2 - t^3$$iii)$$p(x) = x^3$$iv)$$p(x) = (x - 1)(x + 1)$$

i)$$p(y) = y^2 - y + 1$$

Firstly, let us put x = 0,
$$\therefore p(0) = 0^2 - 0 +1$$
$$\Rightarrow p(0) = 1$$

Now, let us put x = 1,
$$\therefore p(1) = 1^2 - 1 +1$$
$$\Rightarrow p(1) = 1$$

Now, let us put x = 2,
$$\therefore p(2) = 2^2 - 2 +1$$
$$\Rightarrow p(2) = 4 - 2 +1$$
$$\Rightarrow p(2) = 3$$

ii)$$p(t) = 2 + t + 2t^2 - t^3$$

Firstly, let us put x = 0,
$$\therefore p(0) = 2 + 0 + 2{0}^2 - {0}^3$$
$$\Rightarrow p(0) = 2$$

Now, let us put x = 1,
$$\therefore p(1) = 2 + 1 + 2{1}^2 - {1}^3$$
$$\Rightarrow p(1) = 3 + 2 - 1$$
$$\Rightarrow p(1) = 4$$

Now, let us put x = 2,
$$\therefore p(2) = 2 + 2 + 2{2}^2 - {2}^3$$
$$\Rightarrow p(2) = 4 + 8 - 8$$
$$\Rightarrow p(2) = 4$$

iii)$$p(x) = x^3$$

Firstly, let us put x = 0,
$$\therefore, p(0) = {0}^3$$
$$\Rightarrow p(0) = 0$$

Now, let us put x = 1,
$$\therefore p(1) = {1}^3$$
$$\Rightarrow p(1) = 1$$

Now, let us put x = 2,
$$\therefore p(2) = {2}^3$$
$$\Rightarrow p(2) = 8$$

iv)$$p(x) = (x - 1)(x + 1)$$

Firstly, let us put x = 0,
$$\therefore p(0) = (0 - 1)(0 + 1)$$
$$\Rightarrow p(0) = -1$$

Now, let us put x = 1,
$$\therefore p(1) = (1 - 1)(1 + 1)$$
$$\Rightarrow p(1) = 0$$

Now, let us put x = 2,
$$\therefore, p(2) = (2 - 1)(2 + 1)$$
$$\Rightarrow p(2) = 1 × 3$$
$$\Rightarrow p(2) = 3$$