How do you divide #(2x^4 + 5x^3 - 2x^2 + 5x + 3)/(x-1)#?

1 Answer
Apr 24, 2017

Answer:

Long division or synthetic division
#2x^3 + 7x^2 +5x + 10 +13/(x-1)#

Explanation:

Given:#(2x^4+5x^3-2x^2+5x+3)/(x-1)#

Long Division:

#" "2x^3 + 7x^2 +5x + 10 + 13/(x-1)#
#x-1|bar(2x^4 + 5x^3 -2x^2 + 5x + 3) #
#" "ul(2x^4-2x^3)#
#" "7x^3 - 2x^2#
#" "ul(7x^3-7x^2 )#
#" "5x^2 + 5x#
#" "ul(5x^2-5x)#
#" "10x + 3#
#" "ul(10x-10)#
#" "13#

Synthetic Division , where #x-1 = 0" or " x = 1:#

terms:#" "x^4" "x^3" "x^2" "x" constant"#

#ul(1)| " "2" "5" "-2" "5" "3#
#" "ul(+" "2" "7" "5" "10)#
#" "2" "7" "5" "10" "13#

terms:#" "x^3" "x^2" "x" constant, remainder"#

This means

#(2x^4+5x^3-2x^2+5x+3)/(x-1) = 2x^3 + 7x^2 +5x + 10 +13/(x-1)#