A cube has a surface area of 6x^2+48x+96

Question

Find the length of a side. (First factor out the GCF.)

The length of the side is what?

Answer 1

First note that a cube is a prism made of 6 square faces.

The surface area of a cube is given by the following formula:   SA = 6a²

     where a² is the area of one of the square faces (since a square has 4 equal sides its area is the square of one of the sides).

We are given that the surface area of the cube is   6x² + 48x + 96 ,   so we set this equal to 6a² and solve for a which is the length of one of the sides of the square and thus the cube.

          6x² + 48x + 96 = 6a² 

   factor out a 6 (gcf) from both sides of equation

          6(x² + 8x + 16) = 6(a²) 

   divide both sides of the equation by 6

          x² + 8x + 16 = a² 

   factor the polynomial on the left hand side of the equation

          (x + 4)(x + 4) = a² 

   when multiplying two like terms, add their exponents and keep the common base

          (x + 4)² = a² 

   take the square root of both sides of the equation to solve for a

           x + 4 = a

Thus, the length of each side of the cube is   x + 4