Question

(x 3 - 4x 2 + 4x - 1) ÷ (x -1)

Answer 1

answer :

${x}^{2} - 3x + 1$

Step-by-step 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