The value of `p` for which the polynomial `x^3+4x^2-p x+8` is exactly divisible by `(x-2)` is 0 (b) 3 (c) 5 (d) 16

Explanation

To find the value of \( p \) for which the polynomial \( x^3 + 4x^2 - px + 8 \) is exactly divisible by \( (x - 2) \), we can use the Remainder Theorem. According to this theorem, if a polynomial \( f(x) \) is divisible by \( (x - a) \), then \( f(a) = 0 \).

### Step-by-Step Solution:

1. **Identify the polynomial and the divisor**:
We have the polynomial \( f(x) = x^3 + 4x^2 - px + 8 \) and we want to check for divisibility by \( (x - 2) \).

2. **Set up the equation using the Remainder Theorem**:
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