Question

How do you long divide `(3x^2+x-10) / (6x+1)`?

Answer 1

`color(magenta)(1/2x+1/12`

Explanation:

`color(white)(.)color(white)(..........)ul(1/2x+1/12)`
`6x+1|3x^2+0+x-10`
`color(white)(.............)ul(3x^2+0+1/2x)`
`color(white)(...........................)1/2x-10`
`color(white)(...........................)ul(1/2x+1/12)`
`color(white)(..................................)-10 1/12`

`color(magenta)((3x^2+x-10) / (6x+1) = 1/2x+1/12` and remainder of`color(magenta)((-10 1/12)/(6x+1)`