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3 What is the remainder when the polynomial 1x ^ 3 - 1 is divided by x-2

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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.

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