Question

How do you find the quotient of `(x^3+11x+14)div (x+2)` using long division?

Answer 1

`color(magenta)((x^3+11x+14) / (x+2) = x^2-2x+15` and remainder of `color(magenta)((-16)/(x+2)`

Explanation:

`color(white)(..........)color(white)(.)ul(x^2-2x+15)`
`x+2|x^3+0+11x+14`
`color(white)(............)ul(x^3+2x^2)`
`color(white)(...............)-2x^2+11x`
`color(white)(................)ul(-2x^2-4x)`
`color(white)(..............................)15x+14`
`color(white)(..............................)ul(15x+30)`
`color(white)(...................................)-16`

`color(magenta)((x^3+11x+14) / (x+2) = x^2-2x+15` and remainder of `color(magenta)((-16)/(x+2)`