Q Question
Sandra works in the shippling and logistics department at in online retaller. She and her team are working on a new box design, where the helght of the box is $x-3$.
If the volume of the box is $x^{8}-6 x^{2}+7 x+6$, what is the area of the base?
Use long division to find the area expression, and then select the correct answer. For help, see this worked example $\mathbb{Z}$.
$x^{2}-9 x-20$
$x^{2}-3 x-2$
$x^{2}+3 x+2$
$x^{2}+9 x+20$

Step 1 ：The volume of a box is given by the formula Volume = Base Area * Height. In this case, we are given the volume and the height, and we are asked to find the base area.

Step 2 ：We can find the base area by dividing the volume by the height. The height of the box is given as \(x-3\) and the volume is given as \(x^{8}-6 x^{2}+7 x+6\). So, we need to divide the volume by the height to find the base area.

Step 3 ：The output from the division is a tuple, where the first element is the quotient and the second element is the remainder. The quotient represents the base area of the box. The remainder is not zero, which means that the volume is not exactly divisible by the height. However, since we are asked to find the base area, we can ignore the remainder.

Step 4 ：The base area of the box is given by the expression \(x^{7} + 3x^{6} + 9x^{5} + 27x^{4} + 81x^{3} + 243x^{2} + 723x + 2176\).

Step 5 ：Final Answer: The base area of the box is \(\boxed{x^{7} + 3x^{6} + 9x^{5} + 27x^{4} + 81x^{3} + 243x^{2} + 723x + 2176}\).