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The problem asks for the **Greatest Common Divisor (MCD)** of two polynomials \(F(x)\) and \(P(x)\), evaluated at \(x = 4\).

The two polynomials are given as:

\[
F(x) = x^3 + x^2 - x - 1
\]
\[
P(x) = x^3 - 6x^2 + 11x - 6
\]

### Step 1: Factor the polynomials (if possible).
To find the greatest common divisor (MCD) of the polynomials \(F(x)\) and \(P(x)\), we would normally factor them.

1. **Factorization of \(F(x)\):**

Using synthetic division or factoring techniques:
\[
F(x) = (x - 1)(x^2 + 2x + 1) = (x - 1)(x + 1)^2
\]

2. **Factorization of \(P(x)\):**
Similarly:
\[
P(x) = (x - 1)(x - 2)^2
\]

### Step 2: Find the GCD of the factored forms.

The common factor between \(F(x)\) and \(P(x)\) is \((x - 1)\).

Thus, the greatest common divisor (MCD) of the two polynomials is:
\[
\text{MCD}(F(x), P(x)) = x - 1
\]

### Step 3: Evaluate at \(x = 4\).
Now, evaluate \(x - 1\) at \(x = 4\):
\[
\text{MCD}(4) = 4 - 1 = 3
\]

### Final Answer:
The numerical value of the MCD of the polynomials at \(x = 4\) is **3**, which corresponds to option **d)**.

---

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you perform synthetic division for polynomial factoring?
2. What are the steps to find the GCD of two polynomials manually?
3. How can we confirm that a polynomial factorization is correct?
4. What other methods can be used to solve polynomial GCD problems?
5. Why is the evaluation of the MCD at a specific point important?

**Tip:** When solving polynomial problems, always check for common factors between terms first, as it can simplify the calculations dramatically.

The numerical value of the GCD (MCD) of the polynomials F(x) = x^3 + x^2 - x - 1 and P(x) = x^3 - 6x^2 + 11x - 6 for x = 4, is:

Solve the problem of finding the GCD of the polynomials F(x) = x^3 + x^2 - x - 1 and P(x) = x^3 - 6x^2 + 11x - 6, and evaluate at x = 4. Learn key concepts like polynomial factoring and GCD. Suitable for students in Grades 10-12.

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