If `p(x)=x^(3)-2x^(2)+x+1" then "p(0) xx p(-1)=............`

Answer

To solve the problem, we need to evaluate the polynomial \( p(x) = x^3 - 2x^2 + x + 1 \) at \( x = 0 \) and \( x = -1 \), and then find the product of these two values.

### Step-by-Step Solution:

1. **Evaluate \( p(0) \)**:
- Substitute \( x = 0 \) into the polynomial:
\[ p(0) = 0^3 - 2(0^2) + 0 + 1 \]
- Simplifying this gives:
\[ p(0) = 0 - 0 + 0 + 1 = 1 \]

2. **Evaluate \( p(-1) \)**:
- Substitute \( x = -1 \) into the polynomial:
\[ p(-1) = (-1)^3 - 2(-1)^2 + (-1) + 1 \]
- Simplifying this gives:
\[ p(-1) = -1 - 2 - 1 + 1 \]
- Combining the terms:
\[ p(-1) = -1 - 2 - 1 + 1 = -3 \]

3. **Calculate the product \( p(0) \times p(-1) \)**:
- Now we multiply the two results:
\[ p(0) \times p(-1) = 1 \times (-3) = -3 \]

### Final Answer:
\[ p(0) \times p(-1) = -3 \]