Question

Find the volume of a rectangular prism with a length of x + 8, a width of x – 3, and a height of x – 2. What is its volume expressed as a polynomial?

Answer 1

We know that volume is : Base area times height .

here base is a rectangle : the length and width are : ( x+8) and ( x-3)

Area of the rectangle = length times width

= ( x+8)* ( x-3)

The volume o f the prism = base area times height

= ( x+8)( x-3) * (x-2)

Let us expand it . = ( x * x -3x + 8x - 8* 3 ) ( x-2)

= ( x^2 + 5x - 24)( x-2)

= x^2* x - 2x^2 + 5x* x - 5x* 2 - 24x -24*-2

= x^3 - 2x^2 + 5x^2 -10x -24x + 48

= x^3 + 3x^2 - 34x + 48

This is the expression for volume .