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

1 Answer
Apr 24, 2017

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)