Question

How do you long divide `2n^3 - 14n + 12 div n + 3`?

Answer 1

Quotient is `2n^2-6n+4` and remainder is `0`

Explanation:

`2n^3-14n+12`

=`2n^3+6n^2-6n^2-18n+4n+12`

=`2n^2*(n+3)-6n*(n+3)+4*(n+3)`

=`(2n^2-6n+4)*(n+3)`

Hence quotient is `2n^2-6n+4` and remainder is `0`.

Answer 2

`color(green)("Quotient " 2*(n^2 - 3n + 2), color(indigo)(" Remainder " 0`

Explanation:

`color(white)(aaa aaa aaa aaa aa) 2n^2 color(white)(aa)- 6n color(white)(aaa) + 4`
`color(white)(aaa aaa aaa ) | - - - - - - - - - - -`
`color(white)(aaa) n + 3 " "color(aaa)| color(white)(aaa)2n^3 color(white)(aaa aa) 0 color(white)(aa)-14n color(white)(aa) + 12`
`color(white)(aaa aaa aaa ) | color(white)(aaa a)2n^3 color(white)(a)+ 6n^2`
`color(white)(aaa aaa aaa) | - - - - - - - - -`
`color(white)(aaa aaa aaa) | color(white)(aaa aaa) 0 color(white)(a)-6n^2 color(white)(a)-14n`
`color(white)(aaa aaa aaa) | color(white)(aaa aa a aa)-6n^2 color(white)(a) - 18n`
`color(white)(aaa aaa aaa) | color(white)(aaa aa) - - - - - - - - -`
`color(white)(aaa aaa aaa) | color(white)(aaa aaa aaa aaa) 0 color(white)(aa) + 4n color(white)(aaa) + 12`
`color(white)(aaa aaa aaa) | color(white)(aaa aaa aaa aaa aaa) +4n color(white)(aaa) + 12`
`color(white)(aaa aaa aaa) | color(white)(aaa aaa aaa a) - - - - - - -`
`color(white)(aaa aaa aaa) | color(white)(aaa aaa aaa aaa aaa aaa ) 0 color(white)(aaa aaa a) 0`

`color(green)("Quotient " 2n^2 - 6n + 4), color(indigo)(" Remainder " 0`