Question

Polynomial long division​

Answer 1

You're dividing
`2x^3-2x^2+3x-4` (1) by
`x+1` (2).

`2x^3=2x^2\cdot x`, and
`2x^2(x+1)=2x^3+2x^2` (3). Subtract this from (1) to get a remainder of

`(2x^3-2x^2+3x-4)-(2x^3+2x^2)=-2x^2+3x+4` (4)

`-2x^2=-2x\cdot x`, and
`-2x(x+1)=-2x^2-2x` (5). Subtract this from (4) to get a new remainder of

`(-2x^2+3x+4)-(-2x^2-2x)=5x+4` (6)

`5x=5\cdot x`, and
`5(x+1)=5x+5` (7). Subtract this from (6) to get a new remainder of

`(5x+4)-(5x+5)=-1` (8)

`-1` doesn't contain any factors of
`x`, so we're done and we've shown

`(2x^3-2x^2+3x-4)/(x+1)=2x^2+(-2x^2+3x+4)/(x+1)`

`(2x^3-2x^2+3x-4)/(x+1)=2x^2-2x+(5x+4)/(x+1)`

`(2x^3-2x^2+3x-4)/(x+1)=2x^2-2x+5-\frac1{x+1}`

so that the quotient is
`2x^2-2x+5` (9).