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.