Question

How do you use synthetic division to divide `(3x^3-4x^2+5)/(x-3/2)`?

Answer 1

The remainder is `=49/8` and the quotient is `=3x^2+1/2x+3/4`

Explanation:

We perform the synthetic division

`color(white)(aaaa)` `3/2` `color(white)(aaaa)` `|` `color(white)(aaaa)` `3` `color(white)(aaaa)` `-4` `color(white)(aaaaa)` `0` `color(white)(aaaaaa)` `5`

`color(white)(aaaaaa)` `color(white)(aaaa)` `|` `color(white)(aaa)` `color(white)(aaaaaaaa)` `9/2` `color(white)(aaaa)` `3/4` `color(white)(aaaa)` `9/8`

`color(white)(aaaaaaaaaa)`------------------------------------------------------------

`color(white)(aaaa)` `color(white)(aaaaaa)` `color(white)(aaaaaa)` `3` `color(white)(aaaaa)` `1/2` `color(white)(aaaaa)` `3/4` `color(white)(aaaaa)` `color(red)(49/8)`

The remainder is `=49/8`

The quotient is `=3x^2+1/2x+3/4`

Verification, by using the remainder theorem

`f(3/2)=81/8-9+5=81/8-4=49/8`