pre calculus

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solve the following equation in the complex number system Please show all your work.
5x^5 + 32x^4 - 5x - 32 = 0

  • pre calculus -

    A little synthetic division shows

    5x^5 + 32x^4 - 5x - 32
    = (x-1)(x+1)(5x^3 + 32x^2 + 5x + 32)
    Notice the 5,32 5,32 coefficients.
    a little regrouping gives

    (x-1)(x-1)(x^2(5x+32) + (5x+32))
    (x-1)(x+1)(x^2 + 1)(5x+32)

    Actually, we could have saved ourselves the synthetic division by noticing the 5,32,5,32 grouping at first:

    (x^4 - 1)(5x+32)

    You can probably take it from here . . .

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