Answer: 3x²−13x−22 −19/x−1.
Original Equation: 3x³−16x²−9x+3 divided by x-1.
1. Get x-1 to equal x. x-1+1=0+1, x=1.
2. Use the lead coefficients of each term and if there is a missing term in between two lets say for example x³and x. x² should be between these two terms, but since it is not, we would put 0 as the leading coefficient. In this problem there’s no missing terms, so we will be able to use the leading coefficients.
3. Set it up for synthetic division as shown.
[1] 3 -16 -9 3
4. The steps to complete synthetic division is bring down the 3 and multiply it by the divisor which is the 1. Once you multiply it by 1, add it to the -16 which will get you -13. Then multiply -13×1 to get -13, so you would subtract -9-13 to get -22. Lastly bring down the -22 and multiply it by the divisor 1 to get -22 then subtract it with 3 to get -19.
5. Once you get the last solution you will recreate the equation, but instead of starting out with x³ you will start out with x². Also you will use the results from the synthetic division as your lead coefficients to the equation, so the new equation for this problem would be 3x²−13x−22.
6. The next part is the remainder which is -19 so how they want you to write this is by putting the remainder over the x-1 equation in fraction form. So it is going to look like this −19/x−1.
7. The final answer is 3x²−13x−22 −19/x-1.