Question

How do you find the quotient of `(c^3-27)div(c-3)`?

Answer 1

`c^2 + 3 c + 9`

Explanation:

we use a long division to solve it.

`c^3 -27` `--->c^2 * (c -3)`
`-(c^3 - 3 c^2)`
.................................
`3 c^2 - 27` `---> 3 c * (c -3)`
`-(3 c^2 - 9 c)`
.................................
`9 c - 27` `---> 9 * (c -3)`
`-(9 c - 27)`
...............................
`0`

the answer is `c^2 + 3 c + 9`

Answer 2

`c^2+3c+9`

Explanation:

The numerator is a `color(blue)"difference of cubes"` and in general is factorised as shown.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(2/2)|)))`

`c^3-27=(c)^3-(3)^3rArra=c" and " b=3`

`rArrc^3-27=(c-3)(c^2+3c+9)`

`rArr(c^3-27)/(c-3)=(cancel((c-3)^1)(c^2+3c+9))/(cancel((c-3)^1)`

`=c^2+3c+9larrcolor(red)" quotient"`