(h^2+h-12) divided by (h+4) synthetic division
all that work, and you end up with a wrong answer!
...
| 1 -3
| 12 0
(h^2 + h - 12) divided by (h + 4) equals h - 3
I apologize for the error in my previous response. You are correct. The correct answer is (h^2 + h - 12) divided by (h + 4) equals h - 3. Thank you for pointing out the mistake.
To perform synthetic division for dividing a polynomial by a linear binomial, such as (h^2 + h - 12) divided by (h + 4), follow these steps:
Step 1: Write the coefficients of the dividend polynomial in descending order of powers of h. In this case, the dividend polynomial is h^2 + h - 12, so the coefficients are 1, 1, and -12.
Step 2: Set up the division table. Write the divisor, h + 4, to the left side of the table, and then write the coefficients of the dividend polynomial in the top row.
| 1 | 1 | -12
-----------------------------------
-4 |
Step 3: Bring down the first coefficient of the dividend polynomial (-4 in this case) into the last row of the table.
| 1 | 1 | -12
-----------------------------------
-4 | -4
Step 4: Multiply the divisor, h + 4, by the number in the last row (-4) and place the result in the second row.
| 1 | 1 | -12
-----------------------------------
-4 | -4
-----------
|
Step 5: Add the numbers in the second row.
| 1 | 1 | -12
-----------------------------------
-4 | -4
-----------
| -3
Step 6: Multiply the divisor, h + 4, by the number in the last row (-3) and place the result in the third row.
| 1 | 1 | -12
-----------------------------------
-4 | -4 | -12
-----------
| -3
Step 7: Add the numbers in the third row.
| 1 | 1 | -12
-----------------------------------
-4 | -4 | -12
-----------
| -3 | -12
Step 8: The rightmost number in the last row, -12, represents the remainder of the division.
Step 9: The numbers in the first, second, and third rows (1, -3, -12) represent the coefficients of the quotient polynomial.
Therefore, the result of dividing (h^2 + h - 12) by (h + 4) using synthetic division is h - 3 with a remainder of -12.
To divide the polynomial h^2 + h - 12 by h + 4 using synthetic division, follow these steps:
1. Write the polynomial in descending order of powers:
h^2 + h - 12
2. Set up the synthetic division table. Place -4 (opposite sign of h+4) in the top left box and write the coefficients of the polynomial in the top row, starting from the highest power and moving to the right. Leave a space for the constant term at the end.
-4 | 1 1 -12
3. Bring down the first coefficient (1) directly below the line.
-4 | 1 1 -12
|__
| 1
4. Multiply -4 by 1 and write the result (product) underneath the next coefficient (-12).
-4 | 1 1 -12
|__ -4
| 1
5. Add the two numbers in the same column.
-4 | 1 1 -12
|__ -4
| 1 -3
6. Multiply -4 by -3 and write the product underneath the last coefficient.
-4 | 1 1 -12
|__ -4
| 1 -3
| 12
7. Add the two numbers in the same column.
-4 | 1 1 -12
|__ -4
| 1 -3
| 12 0
The result is a quotient of h + 1 and a remainder of 0. Therefore, (h^2 + h - 12) divided by (h + 4) equals h + 1.