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Thread: Use the given zero to find the remaining zeros of each polynomial function

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    Use the given zero to find the remaining zeros of each polynomial function

    Finding the zero's of P(x) 3x^3-29x^+92x+34. The given zeros are 5+3i
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    Quote Originally Posted by renebran View Post
    Finding the zero's of P(x) 3x^3-29x^+92x+34. The given zeros are 5+3i
    If 5 + 3i is a zero, then so is 5 - 3i.


    So x - (5 + 3i) and x - (5 - 3i) are factors.

    Therefore so is [x - (5 + 3i)][x - (5 - 3i)]

     = x^2 - x(5 - 3i) - x(5 + 3i) + (5 + 3i)(5 - 3i)

     = x^2 - 5x + 3ix - 5x - 3ix + 25 + 9

     = x^2 - 10x + 34.


    So divide your polynomial by x^2 - 10x + 34 in order to find the third factor (and third zero).
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    Quote Originally Posted by Prove It View Post
    If 5 + 3i is a zero, then so is 5 - 3i.


    So x - (5 + 3i) and x - (5 - 3i) are factors.

    Therefore so is [x - (5 + 3i)][x - (5 - 3i)]

     = x^2 - x(5 - 3i) - x(5 + 3i) + (5 + 3i)(5 - 3i)

     = x^2 - 5x + 3ix - 5x - 3ix + 25 + 9

     = x^2 - 10x + 34.


    So divide your polynomial by x^2 - 10x + 34 in order to find the third factor (and third zero).
    This is where I'm having the problem. I'm not sure how to divide the polynomial .
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    Quote Originally Posted by renebran View Post
    This is where I'm having the problem. I'm not sure how to divide the polynomial .
    Use long division.
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