Question

Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x.

(x 3 - 4x 2 + 4x - 1) ÷ (x -1)

Answer 1

The given division is

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

To divide this using synthetic division we first need to right it down in a division-like format. We do that, by just using coefficients of the dividend, in this case, 1, -4, 4 and -1.

Then, we right down the first coefficient as it's shown in the first image. As second step, we must multiply the entry in the left part of the division format by each entry under the horizontal line, this results we write it down under the next coefficient and do the sum, this process repeats over and over until we get zero as a result of the synthetic division.

The second image shows the complete process, which give the result.

Therefore, the division is

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

Answer 2

The quotient is
`x^2-3x+1`

Explanation:

The given polynomial division is
`(x^3-4x^2+4x-1)/ (x-1)`

To perform the synthetic division we write out the coefficients and arrange them as shown.

1 -4 4 -1

1 | 1 -3 1

1 -3 1 0

The quotient is
`x^2-3x+1`

The descending powers of x means from highest degree to the least

The remainder is 0