A rectangular prism has a volume of 8x^3+14x^2+x-2 and a height of 2x+1. Which expression represents the area of the base of the prism?
A. 4x^2+5x-2
B. 4x^2+5x+2
C. 4x^2+9x+4
D. 4x^2+9x+5

Thanks in advance
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1 Answer

Area of base times height=volume.
So area=vol/height=(8x^3+14x^2+x-2)/(2x+1)=4x^2+5x-2, option A.
(Quick tip: put x=1. Volume becomes 21, height=3, 21/3=7=4+5-2=area. None of the other options gives an area of 7. Also works putting x=0: -2/1=-2. Option A only fits.)
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