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What is the remainder when 3x^3−x^2+2x−4
is divided by (x - 2)?

The remainder is _______________________

1 Answer

6 votes

Explanation:

To find the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2), we can use synthetic division.

First, we write the coefficients of the polynomial in descending order of powers of x, with any missing terms represented by a coefficient of 0:

3 1 -1 2 -4

To perform synthetic division, we bring down the first coefficient (1) and multiply it by the divisor (x - 2) to get the first entry in the second row, which we then add to the second coefficient:

3 1 -1 2 -4

1

1

We repeat the process with the new coefficient in the third row, multiplying it by the divisor and adding it to the next coefficient:

3 1 -1 2 -4

1 3

1 2

Finally, we repeat the process with the new coefficient in the third row to get the last entry in the second row:

3 1 -1 2 -4

1 3 8

1 2 4

The last entry in the third row is the remainder, which is 4. Therefore, the remainder when 3x^3 - x^2 + 2x - 4 is divided by (x - 2) is 4.

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