How do I use the remainder theorem to divide 2x^2-5x-12x25x1 by x-4x4?

1 Answer
Feb 28, 2016

2x+3+11/(x-4)2x+3+11x4

Explanation:

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

color(white)(4.)|4.color(white)(.)2color(white)(..)-5color(white)(..)-1.2..5..1
4color(white)(.)|4._________

This becomes
color(white)(4.)|4.color(white)(.)2color(white)(..)-5color(white)(..)-1.2..5..1
4color(white)(.)|4.____88______1212_
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)