Question

How do you divide `4x^3 + 3x + 5` by `2x-3`?

Answer 1

`(4x^3+3x+5)/(2x-3)=2x^2+3x+6+23/(2x-3)`

Explanation:

First rearrange from the highest degree term to the lowest

both dividend `(4x^3+3x+5)=(4x^3+0*x^2+3x+5)` and divisor `(2x-3)`

`" " " " " " " "underline(2x^2+3x+6" " " " " " " " ")`
`2x-3" "|~4x^3+0*x^2+3x+5`
`" " " " " " " "underline(4x^3-6x^2" " " " " " " " " ")`
`" " " " " " " " " " " " " "6x^2+3x+5`
`" " " " " " " " " " " " " "underline(6x^2-9x" " " " " )`
`" " " " " " " " " " " " " " " " " " "12x+5`
`" " " " " " " " " " " " " " " " " " "underline(12x-18)`
`" " " " " " " " " " " " " " " " " " " " " " " 23" " "`the remainder

so that the final answer

`"dividend"/"divisor"="quotient"+"remainder"/"divisor"`

`(4x^3+3x+5)/(2x-3)=2x^2+3x+6+23/(2x-3)`