Given:
p(x) = x^3 - x^2 + 1

To find:
p(1) and p(-1)/2

Solution:

Step 1: Evaluate p(1)
To find p(1), we substitute x = 1 in the given polynomial:

p(1) = (1)^3 - (1)^2 + 1
= 1 - 1 + 1
= 1

Therefore, p(1) = 1.

Step 2: Evaluate p(-1)/2
To find p(-1)/2, we substitute x = -1 in the given polynomial:

p(-1)/2 = (-1)^3 - (-1)^2 + 1
= -1 + 1 + 1
= 1

Therefore, p(-1)/2 = 1.

Summary:
- p(1) = 1
- p(-1)/2 = 1

Explanation:
- The given polynomial, p(x) = x^3 - x^2 + 1, represents a cubic polynomial.
- To find p(1), we substitute x = 1 in the polynomial and evaluate the expression.
- Similarly, to find p(-1)/2, we substitute x = -1 in the polynomial and evaluate the expression.
- By performing the calculations, we find that both p(1) and p(-1)/2 have a value of 1.
- This means that when x is 1 or -1, the given polynomial evaluates to 1.
- The evaluation of p(x) at specific values helps us understand the behavior and properties of the polynomial.