Find the Synthetic Division:
(10x^4-50x^3-800)/(x-6)
hard to show in this format, since the numbers do not line up nicely
6 | 10 -50 0 0 -800
...........60 60 360 2160
..... 10 10 60 360 1360
To perform synthetic division, follow these steps:
Step 1: Write down the coefficients of the polynomial in descending order. In this case, the polynomial is 10x^4 - 50x^3 - 800. So the coefficients are 10, -50, 0, 0, and -800.
Step 2: Identify the divisor and set it equal to zero. In this case, the divisor is x - 6. Set it equal to zero:
x - 6 = 0
Step 3: Solve for x by adding 6 to both sides:
x = 6
Step 4: Set up the synthetic division table. Write down the divisor and the solution for x as the first row of the table. In this case:
6 | 10 -50 0 0 -800
Step 5: Bring down the first coefficient (10) to the bottom row of the table:
6 | 10 -50 0 0 -800
10
Step 6: Multiply the divisor (6) by the number at the bottom of the column (10), and write the result in the next column:
6 | 10 -50 0 0 -800
10
60
Step 7: Add the result from the previous step (60) to the next coefficient (-50), and write the sum in the next column:
6 | 10 -50 0 0 -800
10
60
10
Step 8: Repeat steps 6 and 7 for each coefficient in the polynomial:
6 | 10 -50 0 0 -800
10
60
10 60
...
Keep repeating steps 6 and 7 until all coefficients in the polynomial have been accounted for. The final row in the table represents the quotient of the polynomial.
Thus, the synthetic division is as follows:
Quotient: 10x^3 + 60x^2 + 360x + 2160
Remainder: -567