Question

Sandra works in the shipping and logistics department at an online retailer. she and her team are working on a new box design, where the height of the box is x - 3. if the volume of the box is x³ - 6x² + 7x + 6, what is the area of the base? use long division to find the area expression.

A) x² - 9x - 20
B) x² - 3x - 2
C) x² + 3x + 2
D) x² + 9x + 20

Answer 1

Sandra can find the area of the box base by dividing the volume x³ - 6x² + 7x + 6 by the height x - 3. After performing long division, the area of the base is x² - 3x - 2 (Option B).

Step-by-step explanation:

To find the area of the base, we need to divide the volume of the box, x³ - 6x² + 7x + 6, by its height, x - 3. We will use long division to do this.

1. Start by setting up the long division, with x³ - 6x² + 7x + 6 inside the division bracket and x - 3 outside.
2. Divide the first term of the dividend (x³) by the first term of the divisor (x) to get x². Multiply x - 3 by x² and subtract the result from the dividend.
3. Bring down the next term of the dividend and divide again, repeating the steps until you've accounted for all terms of the dividend.
4. The quotient you obtain from this division gives the area of the base.

After doing long division, the quotient is x² - 3x - 2, which represents the area of the base of the box. Therefore, the correct answer is B) x² - 3x - 2.