Question

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

Answer 1

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)`