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The problem asks to find the result of subtracting two polynomials, \( P(x) - Q(x) \), where:

- \( P(x) = 4x^3 + 3x^2 - 7x - 6 \)
- \( Q(x) = x^3 + 2x^2 - 4x + 8 \)

To subtract these two polynomials, we subtract the corresponding terms of the same degree:

\[
P(x) - Q(x) = (4x^3 + 3x^2 - 7x - 6) - (x^3 + 2x^2 - 4x + 8)
\]

### Step-by-step subtraction:

1. **Cubic terms:**
   \[
   4x^3 - x^3 = 3x^3
   \]

2. **Quadratic terms:**
   \[
   3x^2 - 2x^2 = x^2
   \]

3. **Linear terms:**
   \[
   -7x - (-4x) = -7x + 4x = -3x
   \]

4. **Constant terms:**
   \[
   -6 - 8 = -14
   \]

Thus, the result of \( P(x) - Q(x) \) is:
\[
3x^3 + x^2 - 3x - 14
\]

### Answer: Option D

Let me know if you would like further details or have any questions.

Here are 5 related questions to practice:

1. What is the result of adding two polynomials instead of subtracting?
2. How do you find the derivative of \( P(x) \) and \( Q(x) \)?
3. What happens if the degree of the polynomials being subtracted is different?
4. Can you solve \( P(x) = Q(x) \) for the roots of the equation?
5. How would the process change if we were multiplying \( P(x) \) and \( Q(x) \)?

**Tip:** When subtracting polynomials, be mindful of negative signs, especially for constants.

Diketahui polinomial P(X) = 4x^3 + 3x^2 - 7x - 6 dan Q(X) = x^3 + 2x^2 - 4x + 8. Hasil P(X) - Q(X) adalah?

Learn how to subtract two polynomials, P(x) = 4x^3 + 3x^2 - 7x - 6 and Q(x) = x^3 + 2x^2 - 4x + 8, using a detailed step-by-step approach. This problem involves key algebraic concepts and is suitable for students in Grades 10-12.

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