if i divide 2i by x^3-3x^2+4x-12 using synthetic division what is my answer

Question

i am trying to find the answer to this synthetic division problem.

Answer 1

The polynomial function is and the root is 2i

Use synthatic division to find

Step - 1

Write the terms of the dividend so that the degrees of the terms are in descending order.

Then write just the coefficients as shown at the right.

Step - 2:

Write the constant r of the divisor (x - r) to the left. In this case, r = 2i. Bring the first coefficient, 1, down.

Step - 3:

Multiply the first coefficient by r : 2i*1 = 2i.

Write the product under the second coefficient, -3 and : - 3 + 2i.

Multiply the sum, - 3+2i, by r : 2i * (- 3 + 2i) = - 6i - 4.

Write the product under the next coefficient, 4 and add : - 6i - 4 = -6i.

Step -  5:

Multiply the sum,-6i, by r : 2i*-6i = 12 .

Write the product under the next coefficient, -12 and add : - 12 + 12 = 0. The remainder is 0.

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