Final answer:
The volume of a rectangular box with length (x+4), width (x-2), and height (3x+5) is found by multiplying these dimensions to get V = 3x³ + 11x² - 14x - 40. The constant in the final expression is -40.
Step-by-step explanation:
To find the volume of a rectangular box, you multiply the length, width, and height together. In this case, the volume formula V = (x+4)(x-2)(3x+5) needs to be expanded. Let's expand this expression step by step.
First, we'll deal with the length and width: (x+4)(x-2) = x² - 2x + 4x - 8 = x² + 2x - 8.
Next, we have to multiply this result by the height (3x+5). Doing so gives us the final expression of the volume:
V = (x² + 2x - 8)(3x + 5).
Let's now expand this further:
- x²(3x) + x²(5)
- 2x(3x) + 2x(5)
- -8(3x) - 8(5)
Which simplifies to: V = 3x³ + 5x² + 6x² + 10x - 24x - 40.
Combining like terms, we have: V = 3x³ + 11x² - 14x - 40.
The constant in the final expression of the volume is -40. Therefore, the correct answer to what represents the constant in the final answer is:
D) 40