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

1 Answer
Rachel
Feb 28, 2016

#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)#

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