A treasure chest has a volume of x3 + 9x2 + 26x + 24 cm3 and the height is x + 4 cm. Find the polynomial that would represent the area of the bottom of the treasure chest? Explain your reasoning.

Question

A treasure chest has a volume of x3  + 9x2 + 26x + 24 cm3 and the height is x + 4 cm. Find the polynomial that would represent the area of the bottom of the treasure chest? Explain your reasoning.

anonymous · Answer

volume = $$x ^{3} + 9x^{2} + 26x + 24$$
height = x + 4

The bottom area of the chest would be length times width.

Since: Volume = length x width x height
$$\frac{length * width * height}{height} = length * width$$

anonymous · Answer

so just divide out x + 4?

anonymous · Answer

Yep. volume / height = area of the bottom