Question

A rectangular box is x feet long and x feet wide. the volume of the box is (4x8 + 3x6) cubic feet. what polynomial represents the height of the box in feet?

a. 4x + 3
b. 4x6 + 3x4
c. 4x8 + 3x6
d. 4x7 + 3x5

Answer 1

Answer: b. 4x^6 + 3x^4

Explanation:

Answer 2

The volume of the rectangular box is width*length*height.

Let h = height of the box.
Therefore
x*x*h = 4x^8 + 3x^6

Note that 1/x^2 = x^(-2).
Also, (x^a)*(x^b) = x^(a+b)
Therefore
h = 4(x^8)(x^-2) + 3(x^6)(x^-2)
= 4 x^6 + 3x^4

Answer: b. 4x^6 + 3x^4