Question

How do you divide `(2x^3 - 6x^2 + 8) / (x^2 - 4)`?

Answer 1

Explanation:

`(2x^3-6x^2+8)/(x^2-4)`

`color(white)(........)color(white)(.)2x-6`
`x^2-4|overline(2x^3-6x^2 color(white)(......)+8)`
`color(white)(............)ul(2x^3 color(white)(.........)-8x`
`color(white)(................)-6x^2+8x+8`
`color(white)(..................)ul(-6x^2 color(white)(.......)+24)`
`color(white)(..............................)8x-16`

`(2x^3-6x^2+8) / (x^2-4) = 2x-6` and remainder of `(8x-16)/(x^2-4)`