Final answer:
To divide 4x4 + 12x3 + 18x2 + 19x + 9 by x + 1 using synthetic division, set up the synthetic division table and perform the division.
Step-by-step explanation:
Synthetic division is a method used to divide a polynomial by a linear factor. To use synthetic division to divide 4x4 + 12x3 + 18x2 + 19x + 9 by x + 1, we set up the synthetic division table as follows:
-1 │ 4 12 18 19 9
│ -4 -8 -10 -9
─────────────────
4 8 10 9 ¯¯¯¯¯¯¯
The result is 4x3 + 8x2 + 10x + 9.