Question

How do you divide `(p^5+5p^3-11p^2-25p+29)div(p+6)` using synthetic division?

Answer 1

The remainder is `=-9073` and the quotient is `=p^4-6p^3+41p^2-257p+1517`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-6` `color(white)(aaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `0` `color(white)(aaaaa)` `5` `color(white)(aaaa)` `-11` `color(white)(aaaa)` `-25` `color(white)(aaaa)` `29`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaa)` `-6` `color(white)(aaaa)` `36` `color(white)(aaa)` `-246` `color(white)(aaaa)` `1542` `color(white)(aa)` `-9102`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aa)` `-6` `color(white)(aaaa)` `41` `color(white)(aaa)` `-257` `color(white)(aaaa)` `1517` `color(white)(aa)` `color(red)(-9073)`

The remainder is `=-9073` and the quotient is `=p^4-6p^3+41p^2-257p+1517`

`(p^5+5p^3-11p^2-25p+29)/(p+6)=p^4-6p^3+41p^2-257p+1517-9073/(p+6)`