Question

The dimensions for a rectangular prism are `x+2` for the length, `x +3` for the width, and `x` for the height. What the volume of the prism expressed as a polynomial in standard form?

Answer 1

`x^3+5x^2+6x`

Explanation:

The volume of a rectangular prism is given by the formula `V=lwh` where `V` is the volume, `l` is the length, `w` is the width, and `h` is the height.

For this rectangular prism, `V=(x+2)(x+3)(x)`. To put it in standard form it must be multiplied out. `V=(x^2+5x+6)x=x^3+5x^2+6x`

Answer 2

`x^3+5x^2+6x`

Explanation:

We know all the dimensions of the rectangular prism. We need to find its volume

`color(blue)("volume"=lwh`

Whers, `l,w and h` are length,width and height

So,

`rarr(x+2)(x+3)(x)`

Multiply `(x+2) and (x+3)` using the foil method

`rarrx(x^2+5x+6)`

`color(green)(rarrx^3+5x^2+6x`

It is already in the standard form (in decreasing powers)

Hope this helps....! :)