The volume of a rectangular solid is given by the polynomial #8x^4-8x^3-24x^2-3400x# The length of the solid is given by #8x# and the width is given by #x - 5#. Find the height of the solid?

Question

Avery Allen · Accepted Answer

The volume of a rectangular solid is given by the polynomial  #8x^4-8x^3-24x^2-3400x# -The length of the solid is given by #8x# and the width is given by #x - 5#. so the polynomial will have factors  #8x# and #x - 5#  . Factorizing we get #8x^4-8x^3-24x^2-3400x# #=8x(x^3-x^2-3x-425)# #=8x(x^3-5x^2+4x^2-20x+17x-425)# #=8x{x^2(x-5)+4x(x-5)+17(x-25)}# #=8x(x-5)(x^2+4x+17)# #="length"xx"width"xxheight"# So height of the polynomial is #(x^2+4x+17)#

Carson Arnold · Answer

undefined To find the height of the rectangular solid, you can use the formula for the volume of a rectangular solid, which is length times width times height.

Given that the length of the solid is $8x$ and the width is $x - 5$, you can express the volume of the solid as the product of these two expressions multiplied by the height.

So, the volume $V$ can be represented as:

$$V = (8x) \times (x - 5) \times h$$

This simplifies to:

$$V = 8x^2 (x - 5)h$$

Given that the volume of the solid is represented by the polynomial $8x^4 - 8x^3 - 24x^2 - 3400x$, you can equate it to the expression for volume:

$$8x^4 - 8x^3 - 24x^2 - 3400x = 8x^2 (x - 5)h$$

From here, you can solve for $h$ by dividing both sides of the equation by $8x^2(x - 5)$:

$$h = \frac{8x^4 - 8x^3 - 24x^2 - 3400x}{8x^2(x - 5)}$$

Now, simplify the expression to find $h$.