Divide using synthetic division.
(x^4-12x^2-5)/(x+3)
To use synthetic division, we need to set up the problem with coefficients of the polynomial in descending order:
Dividend: x^4 - 12x^2 + 0x - 5
Divisor: x + 3
Now, we will set up the synthetic division table:
-3 | 1 0 -12 0 -5
The first number in the dividend, 1, goes in the leftmost position in the synthetic division table.
Bringing down this 1, we multiply it by -3 to get -3. We write this number under the second column (1st row).
Adding the values in the second column (-3 and 0), we get -3. This sum (-3) is carried over to the third column, and we multiply it by -3 to get 9. Write this value (9) in the third column (2nd row).
Adding the values in the third column (-12 and 9), we get -3. This sum (-3) is carried over to the fourth column, and we multiply it by -3 to get 9. Write this value (9) in the fourth column (3rd row).
Adding the values in the fourth column (0 and 9), we get 9. This sum (9) is carried over to the fifth column, and we multiply it by -3 to get -27. Write this value (-27) in the fifth column (4th row).
Adding the values in the fifth column (-5 and -27), we get -32.
Thus, the result of the division is:
(x^4 - 12x^2 - 5)/(x + 3) = x^3 - 3x^2 + 9x - 27 - 32/(x + 3)