If `p(y)=y^(3)+y^(2)+y+1` find :
(i) y(1) (ii) y(-1)

Answer

To solve the problem, we need to evaluate the polynomial \( p(y) = y^3 + y^2 + y + 1 \) at two specific values: \( y = 1 \) and \( y = -1 \).

### Step-by-Step Solution:

**Step 1: Calculate \( p(1) \)**

Substituting \( y = 1 \) into the polynomial:

\[ p(1) = (1)^3 + (1)^2 + (1) + 1 \]

Calculating each term:

\[ = 1 + 1 + 1 + 1 \]

Adding them together:

\[ = 4 \]

So, \( p(1) = 4 \).

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**Step 2: Calculate \( p(-1) \)**

Now substituting \( y = -1 \) into the polynomial:

\[ p(-1) = (-1)^3 + (-1)^2 + (-1) + 1 \]

Calculating each term:

\[ = -1 + 1 - 1 + 1 \]

Adding them together:

\[ = 0 \]

So, \( p(-1) = 0 \).

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### Final Answers:
(i) \( p(1) = 4 \)
(ii) \( p(-1) = 0 \)