Question

How do you divide `(3p^3-21p^2-p+7)/(3p^2-1)`?

Answer 1

The answer is `=(p-7)`

Explanation:

Let's do the long division
`3p^3-21p^2-p+7` `color(white)(aaaaa)` `∣` `3p^2-1`
`3p^3` `color(white)(aaaaaaa)` `-p` `color(white)(aaaaaaaaa)` `∣` `p-7`
`0` `color(white)(aaa)` `-21p^2` `color(white)(aa)` `0` `color(white)(aaa)` `7`
`0` `color(white)(aaa)` `-21p^2` `color(white)(aaaaaa)` `7` `color(white)(aaaaaaaaa)`

So `(3p^3-21p^2-p+7)/(3p^2-1)=p-7`