Question

(x 3 - 4x 2 + 4x - 1) ÷ (x -1)

Answer 1

`{x}^(2) - 3x + 1`

Explanation:

The explanation is shown in the image

As shown in the image:

1. x divides
`{x}^(3)`=
`{x}^(2)`

2.
`{x}^(2)` multiplies the divisor (x-1) and we obtain
`{x}^(3)-{x}^(2)`

3.
`{x}^(3)-{x}^(2)` substracts from
`{x}^(3)-4{x}^(2)` leaving a remainder of
`-3{x}^(2)`

4. we then stepped 4x down to have
`-3{x}^(2)`+4x

5. x divides
`-3{x}^(2)` gives us -3x

6. we then multiply -3x by (x-1) and subtract it from
`-3{x}^(2)`+4x ,and we obtained x as a remainder

6. we again stepped the -1 down to x-1

7.x -1 divides x-1 gives exactly 1