Question

A rectangular box is x feet long and x feet wide. The volume of the box is (4x^8 + 3x^6) cubic ft. What polynomial represents the height of the box in feet?

Answer 1

Answer:

Hence, the height, in feet, of the rectangular box is given by the polynomial  $h=4x^6+3x^4$

Step-by-step explanation:

The volume of a rectangular box is given by the formula:

$V=length*width*height$

We are given $V=4x^8+3x^6$, length = x, and width = x , plugging these into the formula and figuring out height:

$V=length*width*height\\4x^8+3x^6=(x)(x)(h)\\4x^8+3x^6=x^2h\\h=\frac{4x^8+3x^6}{x^2}\\h=\frac{x^2(4x^6+3x^4)}{x^2}\\h=4x^6+3x^4$

Hence, the height, in feet, of the rectangular box is given by the polynomial  $h=4x^6+3x^4$

Answer 2

$h = \frac{4x^{8} + 3x^{6}}{x^{2}}$
$h = \frac{4x^{8}}{x^{2}} + \frac{3x^{6}}{x^{2}}$
$h = 4x^{6} + 3x^{4}$