Question

Use factoring to find possible dimensions of the container shown. The container is a rectangular prism.

What are the dimensions of the container if x = 3? What is the volume of the container if x = 4?

Answer 1

dimensions: 6 x 7 x 5

volume: 432 ft³

volume of rectangular prism = width * height * length = whl

• given that the volume is 4x³ + 10x² + 4x

factoring the equation:

• 4x³ + 10x² + 4x

• 2x( 2x² + 5x + 2)

• 2x (2x² + 4x + x + 2)

• 2x (2x(x + 2) + 1 ( x + 2))

• 2x (2x+ 1) (x + 2)

comparing we can find that:

• width = 2x

• height = 2x + 1

• length = x + 2

If x = 3, each dimensions:

• width = 2(3) = 6

• height = 2(3) + 1 = 7

• length = 3 + 2 = 5

Volume of container when x = 4,

• width * height * length

• 4x³ + 10x² + 4x

• 4(4)³ + 10(4)² + 4(4)

• 432 ft³