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)
Accepted Solution
A:
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.
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).