Question

The volume of a rectangular solid is given by the polynomial `8x^4-8x^3-24x^2-3400x` The length of the solid is given by `8x` and the width is given by `x - 5`. Find the height of the solid?

Answer 1

The volume of a rectangular solid is given by the polynomial

`8x^4-8x^3-24x^2-3400x`

-The length of the solid is given by `8x` and the width is given by `x - 5`. so the polynomial will have factors `8x` and `x - 5` . Factorizing we get

`8x^4-8x^3-24x^2-3400x`

`=8x(x^3-x^2-3x-425)`

`=8x(x^3-5x^2+4x^2-20x+17x-425)`

`=8x{x^2(x-5)+4x(x-5)+17(x-25)}`

`=8x(x-5)(x^2+4x+17)`

`="length"xx"width"xxheight"`

So height of the polynomial is `(x^2+4x+17)`