Question

How do you divide `(2x^3-5x^2+4x+12)/(x-7)`?

Answer 1

`2x^2+9x+67+481/(x-7)`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(2x^2)(x-7)color(magenta)(+14x^2)-5x^2+4x+12`

`=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(magenta)(+63x)+4x+12`

`=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(red)(+67)(x-7)color(magenta)(+469)+12`

`=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(red)(+67)(x-7)+481`

`"quotient "=color(red)(2x^2+9x+67)", remainder "=481`

`rArr(2x^3-5x^2+4x+12)/(x-7)`

`=2x^2+9x+67+481/(x-7)`

Answer 2

`color(blue)(2x^2+9x+67` plus remainder of `color(blue)481`

Explanation:

`color(white)(.............)ul(color(blue)(2x^2+9x+67)`
`color(white)(aa)x-7` `|` `2x^3-5x^2+4x+12`
`color(white)(..............)ul(2x^3-14x^3)`
`color(white)(........................)9x^2+4x`
`color(white)(........................)ul(9x^2-63x)`
`color(white)(..............................)67x+12`
`color(white)(..............................)ul(67x-469)`
`color(white)(........................................)481`