Help me solve this problem that I missed, so that I can see where I went wrong. Synthetic Division
(3X3 -2x +5). (x-2)
I would set it up with the following algorithm to do synthetic division
(this is how I do it and how I taught it, the ----- are simply there to keep the columns lined up. The first 2 represents your divisor x-2, had it been x+5, I would have used -5. The 3 0 -2 5 are the coefficients of your polynomial)
2 │ 3 0 -2 5
------6 12 20
----3 6 10 25
I brought the 3 down two rows, multiply that first 3 times the number out front, 3x2=6,
I put the 5 under the 0 and added them to get 6.
Now multiply that 6 by the 2 to get 12, placing that 12 under the -2 and add them to get 1
Now 10 times the 2 etc to get 25
Now look at the last row: 3 6 10 25
Since you divided a cubic by a first degree, the answer should be a second degree expression
Your answer will be 3x^2 + 6x + 10 with a remainder of 25
The second line of my explanation has a typo
"I put the 5 under the 0 and added them to get 6"
should have been:
I put the 6 under the 0 and added them to get 6
To solve the problem using synthetic division, follow these steps:
1. Write the polynomial in the dividend form, with the coefficients in descending order. In this case, the polynomial is: 3x^3 - 2x + 5.
2. Identify the divisor, which is x - 2.
3. Set up the synthetic division algorithm as follows:
2 │ 3 0 -2 5
------
Line up the coefficients of the polynomial in descending order.
4. Start the synthetic division:
- Place the divisor, x - 2, on the left side outside the box.
- Write down the coefficients of the polynomial above the line.
2 │ 3 0 -2 5
------
Place the divisor, x - 2, on the left side outside the box.
5. Bring down the first coefficient (3) and write it directly below the line:
2 │ 3 0 -2 5
------
3
Write down the coefficients of the polynomial above the line.
6. Multiply the divisor (2) by the number you brought down (3) and write the result below the next coefficient (0):
2 │ 3 0 -2 5
------
3
6
Multiply 2 by 3 to get 6.
7. Add the two numbers in the second column (0 + 6) and write the sum below:
2 │ 3 0 -2 5
------
3
6
------
3
Add 0 and 6 to get 6.
8. Repeat steps 6 and 7 for the remaining coefficients:
2 │ 3 0 -2 5
------
3 6
6
------
3 6
Multiply 2 by 6 to get 12 and add it to -2 to get 10.
2 │ 3 0 -2 5
------
3 6 10
6
------
3 6 10
Multiply 2 by 10 to get 20 and add it to 5 to get 25.
2 │ 3 0 -2 5
------
3 6 10 25
6
------
3 6 10 25
9. The last row of the synthetic division represents the coefficients of the quotient polynomial. In this case, the resulting polynomial is 3x^2 + 6x + 10. The remainder is 25.
Therefore, the correct answer is:
Quotient = 3x^2 + 6x + 10
Remainder = 25