Final answer:
The remainder when f(x) = x⁶ + 3x - 1 is divided by x + 1 is 0.
Step-by-step explanation:
To find the remainder when dividing f(x) = x⁶ + 3x - 1 by x + 1, we can use synthetic division.
First, set up the synthetic division table:
-1 | 1 0 0 0 0 3 -1
-1 1 -1 1 -1 1 0
The last entry in the bottom row, 0, corresponds to the remainder of the division.
Therefore, the remainder when dividing f(x) by x + 1 is 0.