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

2 Answers
Feb 6, 2017

=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

Feb 6, 2017

(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)