Question

`4x^3-24x^2+29x+15 -: 2x+5` ?

Answer 1

`=4x^3-24x^2+36 1/2x+5`

`36 1/2x` can also be written as `36.5x " or "73/2x`

Explanation:

`4x^3-24x^2+29x+15/2x+5`

As there is no indication of what is required, we might assume it is just simplify.

The only like terms are those in `x`, which need to be added.

`=4x^3-24x^2+29x+7 1/2x+5`

`=4x^3-24x^2+36 1/2x+5`

Answer 2

`(4x^3-24x^2+29x+15)/(2x+5) = 2x^2-17x+57-270/(2x+5)`

Explanation:

I think the question was intended to ask for the result of the division:

`(4x^3-24x^2+29x+15)/(2x+5)`

We can split the numerator into multiples of `(2x+5)` like this:

`4x^3-24x^2+29x+15 = (4x^3+10x^2)-(34x^2+85x)+(114x+285)-270`

`color(white)(4x^3-24x^2+29x+15) = 2x^2(2x+5)-17x(2x+5)+57(2x+5)-270`

`color(white)(4x^3-24x^2+29x+15) = (2x^2-17x+57)(2x+5)-270`

So:

`(4x^3-24x^2+29x+15)/(2x+5) = ((2x^2-17x+57)(2x+5)-270)/(2x+5)`

`color(white)((4x^3-24x^2+29x+15)/(2x+5)) = (2x^2-17x+57)-270/(2x+5)`