Question

The polynomial X^3 + 9x^2 - 22x - 240 expresses the volume, in cubic inches, of a shipping box, and the width is (x+6) in. If the width of the
box is 16 in., what are the other two dimensions? (Hint: The height is greater than the depth.)

Answer 1

Answer:

The dimensions of the box are 38 in by 36 in by 25 in.

Step-by-step explanation:

The volume of the shipping box is given by  

V = x³ + 9x² - 22x - 240

If the width of the box is (x + 6), then it will be a factor of expression of volume, V.

Hence,  

V = x³ + 6x² + 3x² + 18x - 40x - 240

V = x²(x + 6) + 3x(x + 6) - 40(x + 6)

V = (x² + 3x - 40)(x + 6)

V = (x + 8)(x - 5)(x + 6)

So, the length = (x + 8) inches

the depth = (x - 5) inches

and width  = (x + 6) inches

Now, given that, (x + 6) = 36

⇒ x = 30

Therefore, length = (x + 8) = 38 inches and depth = (x - 5) = 25 inches.

Hence the dimensions of the box are 38 in by 36 in by 25 in. (Answer)