Question

How do you divide `(2n^3+62n-26n^2+4)div(2n-6)` using synthetic division?

Answer 1

The remainder is `=269` and the quotient is `=n^2+34n+89`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `3` `color(white)(aaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `31` `color(white)(aaaaaa)` `-13` `color(white)(aaaaa)` `2`
`color(white)(aaaaaaaaaaaa)`_________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaa)` `3` `color(white)(aaaaaaa)` `102` `color(white)(aaaa)` `267`
`color(white)(aaaaaaaaaaaa)`________

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `34` `color(white)(aaaaaaa)` `89` `color(white)(aaaa)` `color(red)(269)`

The remainder is `=269` and the quotient is `=n^2+34n+89`

`(n^3+31n^2-13n+2)/(n-3)=n^2+34n+89+269/(n-3)`

N.B The numerator and denominator were divided by the common factor `2`