Divide using synthetic division.
(x^4-12x^2-5)(x+3)
To divide (x^4 - 12x^2 - 5) by (x + 3) using synthetic division, we arrange the terms in descending order and set up the synthetic division table:
-3 │ 1 0 -12 0 -5
We start by bringing down the first coefficient, which is 1:
-3 │ 1
Next, we multiply -3 (the divisor) by 1 (the number at the bottom):
-3 │ 1 3
We add the result above to the next coefficient:
-3 │ 1 3 -9
Then, we multiply -3 by -9:
-3 │ 1 3 -9 27
We add the result above to the next coefficient:
-3 │ 1 3 -9 27 0
Finally, we multiply -3 by 0:
-3 │ 1 3 -9 27 0
-3 0 27
______________
1 0 -9 27 27
The result of the synthetic division is the row of numbers at the bottom, which represents the coefficients in descending order. Therefore, the quotient is x^3 + 9x - 27, and the remainder is 27.