Question

How do you divide `(x ^ { 3} - 8x ^ { 2} + 17x - 10) \div ( x - 5)`?

Answer 1

The quotient is `=x^2-3x+2` and the remainder is `=0`

Explanation:

Let `f(x)=x^3-8x^2+17x-10`

Let's perform the synthetic division

`color(white)(aaaa)` `5` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `-8` `color(white)(aaaaa)` `17` `color(white)(aaa)` `-10`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaa)` `5` `color(white)(aaa)` `-15` `color(white)(aaaa)` `10`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `-3` `color(white)(aaaaa)` `2` `color(white)(aaaaa)` `color(red)(0)`

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