Question

How do you use synthetic division to divide `(9x^3-16x-18x^2+32)div(x-2)`?

Answer 1

The quotient is `=9x^2-16` and the remainder is `=0`

Explanation:

Let `f(x)=9x^3-18x^2-16x+32`

Let's perform the synthetic division

`color(white)(aaaa)` `2` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `9` `color(white)(aaaa)` `-18` `color(white)(aaa)` `-16` `color(white)(aaaaa)` `32`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `18` `color(white)(aaaaa)` `0` `color(white)(aaaa)` `-32`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `9` `color(white)(aaaaaa)` `0` `color(white)(aaa)` `-16` `color(white)(aaaaa)` `color(red)(0)`

`f(x)=(x-2)(9x^2-16)+0`