College Algrebra

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How would you use synthetic division to find the quotient and remainder for this problem:

(X^3+3ix^2-4ix-2)/(x+i)

  • College Algrebra -

    The same way you do it normally. Just keep track of the i's and remember that -i^2 = 1

    So, the rows of coeffiicients are (munged by font spacing)

    1 3i -4i -2 (i
    0 i -4 -4i+4
    _____________
    1 4i -4-4i 2-4i

    So that means that

    (x^3 + 3ix^2 - 4ix - 2)/(x-i)
    = x^2 + 4ix - (4+4i) remainder 2-4i

    If you multiply it out, it works.

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