Question

It expression p(x)=8x³-12x²+6x-1, represents the volume of solid cube. Show that shape is cube .Also find its edge if x=1

Answer 1

Volume of a cube=a³ ,where a is the edge.

given volume=8x³-12x²+6x-1
=(2x)³-3(2x)² (1) +3 (2x) (1)²-(1)³
=(2x-1)³
=(2x-1) (2x-1) (2x-1)

⇒edge of the cube =2x-1

if x=1

then (2×1-1)=1

therefore edge is 1

Answer 2

substituting x=1 in p(x)=8x³-12x²+6x-1
 p(x)=8x³-12x²+6x-1
p(1)=8(1)³-12(1)²+6(1)-1
      =8-12+6-1
       =14-13
       =1
thus the edge is 1