Question

Divide the following polynomials using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x3 - 2x2 - 1) ( x - 1)

Answer 1

x^2 - x - 1 - 2 / x - 1

Explanation:

This is the correct answer; hope it helps.

Answer 2

To solve using synthetic division:

Draw an upside down division symbol (I did the best I can given the format). Place the constant of x - 1 (1) on the outside, and the coefficients of x³ - 2x² - 1 on the inside, like so:

| x³ x² x¹ x⁰
1 | 1 -2 0 -1
|
|___________

Next, bring down the first coefficient.

| x³ x² x¹ x⁰
1| 1 -2 0 -1
|
|___________
1

Multiply the number on the outside of the symbol (1) by the coefficient you've just brought down (1). Place that number under the next coefficient to the right.

| x³ x² x¹ x⁰
1| 1 -2 0 -1
| 1
|___________
1

Add the new number (1) to the coefficient above it (-2) and place that number directly underneath it.

| x³ x² x¹ x⁰
1| 1 -2 0 -1
| 1
|___________
1 -1

Continue this process until you've run out of numbers to multiply.

| x³ x² x¹ x⁰
1| 1 -2 0 -1
| 1 -1 -1
|___________
1 -1 -1 -2

The resulting numbers are coefficients. The first three are part of the quotient, and the last one is part of the remainder. The remainder becomes the last coefficient (-2) over the divisor (x - 1).

Answer:
(x³ - 2x² - 1) / (x - 1) = x² - x - 1 + -2/x - 1