Divide using synthetic division
(x^2-5x+6) divided by (x-3)
So the answer is what?
wrong yet again!
(x^2-5x+6) divided by (x-3) equals x - 2
Apologies for the incorrect response earlier. You are correct. The quotient of (x^2-5x+6) divided by (x-3) is x - 2.
To perform synthetic division, follow these steps:
1. Write down the coefficients of the dividend (x^2-5x+6) in descending order. In this case, the coefficients are (1, -5, 6).
2. Set up the synthetic division table. Place the divisor (x-3) on the left side of the table, and write down the first coefficient (1) in the top row of the table, omitting the variable.
| 3 |
3. Bring down the first coefficient (1) below the horizontal line.
| 3 |
1
4. Multiply the divisor (3) by the number below the horizontal line (which is 1), and write the result directly below the next coefficient (which is -5). Add the product to the coefficient.
| 3 |
1
________
1
| 3 |
1
________
1 -2
5. Repeat steps 4 and 5 until you reach the last coefficient.
| 3 |
1
________
1 -2 6
6. Read the final row of numbers below the line. The coefficients from left to right represent the quotient. In this case, the quotient is 1x^1 - 2x^0 + 6, which simplifies to x - 2 + 6.
Thus, (x^2-5x+6) divided by (x-3) is equal to x - 2 + 6/(x-3).
To divide (x^2-5x+6) by (x-3) using synthetic division, we set up the synthetic division grid:
3 | 1 -5 6
- 3
_______
Next, bring down the first coefficient (1) into the bottom row:
3 | 1 -5 6
- 3
_______
1
Next, multiply the divisor (3) by the last number in the bottom row (1), and write the result (-3) in the next column:
3 | 1 -5 6
-3 3
_______
1 -3
Next, add the corresponding numbers in the second and third columns, and write the result (-8) in the next column:
3 | 1 -5 6
-3 3
_______
1 -3
-8
Finally, multiply the divisor (3) by the last number in the bottom row (-8), and write the result (-24) in the next column:
3 | 1 -5 6
-3 3
_______
1 -3
-8
-24
The numbers in the bottom row represent the coefficients of the quotient, so the quotient is 1x - 3. Thus, (x^2-5x+6) divided by (x-3) equals x - 3.