Question

How do you divide `(4a^4 -5a^2 +2a -10 )/(2a- 3)`?

Answer 1

The answer is `2a^3+3a^2+2a+4 +2/(2a-3)`

Explanation:

Let's make a long division
`color(white)(aaa)` `4a^4` `color(white)(aaaaa)` `-5a^2+2a-10` `∣` `2a-3`
`color(white)(aaa)` `4a^4-6a^3` `color(white)(aaaaaaaaaaaaa)` ###∣#`2a^3+3a^2+2a+4`
`color(white)(aaaa)` `0+6a^3-5a^2`
`color(white)(aaaaaa)` `+6a^3-9a^2`
`color(white)(aaaaaaaaa)` `0+4a^2+2a`
`color(white)(aaaaaaaaaaa)` `+4a^2-6a`
`color(white)(aaaaaaaaaaaaaa)` `0+8a-10`
`color(white)(aaaaaaaaaaaaaaaaaa)` `8a-12`
`color(white)(aaaaaaaaaaaaaaaaaaaa)` `0+2`

So the answer is `2a^3+3a^2+2a+4 +2/(2a-3)`