Question

How do I use the remainder theorem to divide `2x^2-5x-1` by `x-4`?

Answer 1

`2x+3+11/(x-4)`

Explanation:

I used synthetic division to solve this, but you can use long division too, if you like.

`color(white)(4.)|` `color(white)(.)2color(white)(..)-5color(white)(..)-1`
`4color(white)(.)|`_____

This becomes
`color(white)(4.)|` `color(white)(.)2color(white)(..)-5color(white)(..)-1`
`4color(white)(.)|`__`8`____`12`_
`color(white)(4....)color(blue)(2)` `color(white)(4.....)color(green)(3)` `color(white)(4....)color(red)(11)`

This is rewritten as `color(blue)(2)x+color(green)(3)+color(red)(11)/(x-4)`