A jewelry box has a volume of x^3 + 7x^2 + 7x – 15 cm3 and the height is x + 3 cm. Find the polynomial that would represent the area of the bottom of the jewelry box? Explain your reasoning.

Question

anonymous · Answer

Do i do synthetic division?

eyust707 · Answer

Yes

anonymous · Answer

okay after performing synthetic division, i got x^2+4x-5

anonymous · Answer

simplify it down to (x-1)(x+5)

anonymous · Answer

Would that represent the area ^^^ ?

eyust707 · Answer

Yes

anonymous · Answer

How can I "explain my reasoning"?

eyust707 · Answer

Well the volume of a box is:

Volume = Length x Width x Height

eyust707 · Answer

in this case 

volume = x^3 + 7x^2 + 7x – 15
and
height  = x + 3

eyust707 · Answer

Volume/height = length x width

eyust707 · Answer

so x^3 + 7x^2 + 7x – 15/x + 3 = length x width

eyust707 · Answer

= the area of the bottom

anonymous · Answer

YOU ARE A GENIUS. thank yo so much @eyust707

eyust707 · Answer

np =)