Divide using synthetic division.
(x^3 + 5x^2 - x - 5) / (x+5)
To divide (x^3 + 5x^2 - x - 5) by (x+5) using synthetic division, we set up the synthetic division table as follows:
-5 | 1 5 -1 -5
Next, we bring down the first coefficient, which is 1.
-5 | 1 5 -1 -5
1
Then, we multiply -5 (the number outside the division bar) by 1 (the number we just brought down), which gives us -5. We write this result under the next coefficient.
-5 | 1 5 -1 -5
1
-5
Next, we add 5 (the result we just obtained) to the next coefficient, 5.
-5 | 1 5 -1 -5
1
-5
0
We continue this process, multiplying -5 by 0 and adding to the next coefficient, -1.
-5 | 1 5 -1 -5
1
-5
0
-5
Finally, we add -5 to -5 to get -10.
-5 | 1 5 -1 -5
1
-5
0
-5
-10
The numbers on the bottom row of the synthetic division table represent the coefficients of the resulting polynomial after the division. The final result is:
(x^3 + 5x^2 - x - 5) / (x+5) = x^2 - 5
Therefore, the quotient is x^2 - 5.