Question

How do you use synthetic division to divide `(5x^3-6x^2+8)div(x-4)`?

Answer 1

The remainder is `=232` and the quotient is `=5x^2+14x+56`

Explanation:

Let's perform the synthetic division

Let `f(x)=5x^3-6x^2+8`

Let's perform the synthetic division

`color(white)(aaaa)` `4` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `5` `color(white)(aaaaaa)` `-6` `color(white)(aaaaaa)` `0` `color(white)(aaaaaaa)` `8`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaa)` `20` `color(white)(aaaaaa)` `56` `color(white)(aaaaa)` `224`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `5` `color(white)(aaaaa)` `14` `color(white)(aaaaaaa)` `56` `color(white)(aaaaa)` `color(red)(232)`

`f(x)=(5x^2+14x+56)+232/(x-4)`

The remainder is `=232`