Question

12. The volume of a cube is given by the polynomial p(x)=
$8 {x}^{3} + 36 {x}^{2}$
+54x + 27 find the possible
expression for the sides of the cube Verify your answer when the length of the cube is 5cm​

Answer 1

Step-by-step explanation:

P(x)  = 8 x³ - 36 x² + 54 x - 27

 Volume of a cube is a perfect cube of  its side.

     By examining the first term  and  the last term of  P(x) we can check if it is a cube of  (2 x  - 3)

           =  (2x)³ + 3 * (2x)² (-3) + 3 (2x) (-3)² + (-3)³

          =  8 x³ - 36 x²  + 54 x - 27

              

hence,  the magnitude of the side is given by :  (2x - 3).

         when side of the cube is = 2x - 3 = 3 cm

           So   x  = (3 + 3) /2 = 3 cm

Substituting in P(x) :   8 (3)³ - 36 (3² ) + 54 (3) - 27

                               = 216 - 324 + 162 - 27  = 27  cm³

     since x³ = 27 cm³,  it verifies