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 ^4 - 3x^3 + 3x^2 - 3x + 6) / (x - 2)

Answer 1

We want to perform the following division using synthetic division

`(x^4-3x^3+3x^2-3x+6)/(x-2)`

This becomes

First we write the problem in a division format as shown below

Next take the following step to perform the division

Now, we have completed the table and we obtained the following coefficients, 1, -1, 1, -1, 4

Note that the first four ( 1, -1, 1, -1) are coefficients of the quotient, while the last one (4) is the coefficient of the remainder.

Hence the quotient is

`x^3-x^2+x-1`

And the remainder is 4.

Hence

`(x^4-3x^3+3x^2-3x+6)/(x-2)=x^3-x^2+x-1+(4)/(x-2)`