Answer:
To find the remainder when the polynomial 1x^3 - 1 is divided by x-2, we can use polynomial long division or synthetic division. Here's how to use synthetic division:
First, we write the divisor x-2 as the opposite of its constant term, which is -2:
-2 | 1 0 0 -1
Next, we bring down the leading coefficient 1:
-2 | 1 0 0 -1
1
Then, we multiply -2 by 1 to get -2, and write it under the next coefficient:
-2 | 1 0 0 -1
1
-2
We add 0 and -2 to get -2:
-2 | 1 0 0 -1
1 -2
-2
We multiply -2 by -2 to get 4, and write it under the next coefficient:
-2 | 1 0 0 -1
1 -2
-2 4
We add -1 and 4 to get 3:
-2 | 1 0 0 -1
1 -2
-2 4
3
Therefore, the remainder when 1x^3 - 1 is divided by x-2 is 3.